CTET Paper 2 Maths & Science 4th Jan 2022 (English-Hindi) (Previous Year Paper)

Development describes the growth of humans throughout their lifespan, from conception to death. It refers to development as patterns of change over time. It does not just involve the biological and physical aspects of growth, but also the cognitive and social aspects associated with development.

Key Points Principle of Development Sequences: Every living being followed a pattern of development. A child also develops in an orderly sequence that is almost similar to all children. there are two principles about the development of a child's body. (a) Proximodistal principle (b) Cephalo-caudal Principle.

• Proximodistal sequence: means that the development proceeds from the central part of the body towards the peripheries. In this sequence, the spinal cord of the individual develops first, and then outward development takes place. 
• For example, babies cut their front teeth before they cut their side ones.
• Thus we can conclude that if Infants first learn to move their torso and then their arms and legs means that he follows the Proximodistal principle of development.

Important Points

• Cephalo-caudal sequence: means that development spreads over the body from head to foot i.e. individual begins to grow from the head region downwards. Sufi first gained control of her head, then she could catch hold of objects, sit, crawl and later she could stand and walk.​

Additional Information Some Principles of development are:

• Principle of Individual Differences: It says that every individual is unique in himself/herself as the heredity and environmental factors make him/her different from others.
• Principle of Generality to Specificity:  The development process starts with general responses shown by the child as s/he passes through the later stages s/ he starts exhibiting specific behaviors.
• Principle of Interrelation: The development of an individual is reflected through the balanced interrelation of all the aspects of life. Development in any aspect affects the other aspect also.
• Principle of Interaction: The principle of interaction suggests that an individual is the product of heredity and environment. In other words, the interaction takes place within and outside forces of the child.

Culture: Culture is defined as the "Culture is a set of rules or standards that, when acted upon by the members of a society, produce behavior that falls within a range of variance the members consider proper and acceptable."

Key Points Characteristics and effects of culture:

• Culture differs according to place, time, community, and race and this is natural.
• Everyone's life is influenced by the culture that surrounds them and adopts it as the same it is.
• Culture can never be the result of any single person's initiative or endeavor nor can it be the consequence of any particular incident at any particular time.
• It can be different from place to place, from conditions, language, traditions, etc.
• childhood is the age in which children experience the difference between cultures, and also get how is the diverse culture make their life different from one another.
• **Thus we can consider that the culture of the child depends on many factors such as economic health, education, location, society, tradition, etc, and these are all experienced by a child in childhood age.**​

Important PointsChildhood refers to the period of the human lifespan, ranging from birth to puberty. It consists of many developmental stages. It is from two years to the age of 10 or 12 years. It consists of two stages i.e. Early & Late Childhood.

• Early Childhood:
• 'Early childhood' lies between the age of '2 to 7 years.
• It is also known as the toy age, pre-gang age, curiosity age, and exploratory age, etc. It is a very crucial period for the overall development of the child.
• Later childhood: 
• Later childhood  is the time period from the age of '7 to 12 years'.
• The signs of puberty usually begin to appear in this stage. It is also known as elementary school-age, troublesome age, gang age, play age, etc.

The development of a child takes place through various stages. Although each stage has an encompassing relationship to other stages, it has its own unique characteristic needs and demands. These stages are as follows: 

• Infancy Period - Birth to 2 years
• Early Childhood - 2 to 5-6 years
• Middle Childhood - 5-6 to 12 years
• Adolescence - 12 to 18 years

Key PointsMiddle Childhood:

• The time period extends from age 6 to age 12 years. During this time, the growth rate is slow but steady.
• Tlie growth in legs accounts for most of the increase in height.
• Children learn motor skills like throwing and running to perfection.
• The child's thinking develops rapidly and his/her store of information grows at a fast pace. School-age children develop closer ties with their peers.
• Children take participation in games, they can solve riddles by their thought processes, focus more on their abilities and try to improve them.
• Children compare their abilities, appearance, and characteristics with those of their peers.
• Comprehension and reading ability are increased when children are given interesting stories to read.
• They are better at recognizing emotions in others and empathizing. with them.
• Thus we can consider that, middle childhood is the age in which children can have an interest in taking part in games, and activities, and also want to improve their ability through their logical thoughts.

Important Points

• Infancy period: During this stage, adjusting to the new non-uterine environment becomes the major goal or focus in the life of the neonate. Adjusting to room temperature. Breathing independently, sucking and swallowing the milk, eliminating body, and waste are prime areas that the newborn needs to master.
• Early childhood period: The period from birth to six years is a time for rapid development. In this stage, the absence of experience and deprivation can be detrimental to growth. Care and stimulation are critical during early childhood or the first three years.
• Later childhood: During this stage children develop marked negativism and because of their desire for independence seldom obey their parents. The child begins going to school and learns the rudiments of knowledge essential for successful adult life. The peer group assumes great significance and children of this age 'crowd together, thus earning the name gang age'.
• Adolescence: Adolescence literally means 'to grow to maturity. It is an intermediary stage between childhood and adulthood characteristically possessing qualities of both stages, although not fully in either of them. The age range is from 12-19 years. It is the threshold to adulthood. There are rapid physical changes taking place including sexual maturity which is attained during adolescence.

The process of learning to internalize the values and norms into itself or the mode of learning to live in society is called the process of socialization. It may be defined more comprehensively as a life-long process of inculcation whereby an individual learns the principles, values, and symbols of the social system in which he participates and the expression of those values and norms in the roles he enacts.

Basically, socialization is of two types or we can say that there are two agencies of socialization which is:

• Primary socialization
• Secondary Socialization

Key PointsSecondary socialization- The process of imbibing norms, values, and behavior patterns of school may be called secondary socialization. Example: How to behave in a church, How to behave in a school, etc.

• There are many agencies of secondary socialization such as Media, newspapers, books, magazines, neighbors, schools, etc.

Hence we can conclude that books, magazines, media, and schools are the secondary agencies of socialization.

Hint

• Primary socialization- Inculcation of norms and values within the family is called primary socialization. Here children want to know themselves and try to find their identity and learn the daily routine tasks of humans.
• Example: Hygiene training, Eating food with utensils, toilet training, etc.
• Immediate Family is the best example of agencies of primary socialization.

Jean Piaget made a systematic study of cognitive development among children of different age groups and he categorized it into different developmental stages. These stages are- Sensory-motor stage, pre-operational stage, concrete operational stage, and Formal Operational stage.​

• Cognitive development is much more than the addition of new facts and ideas to an existing store of information.  According to Piaget, our thinking processes change radically, though slowly, from birth to maturity because we constantly strive to make sense of the world.​

Key Points

• ​Piaget identified four factors that influence the development of a child and these are Maturation, Activity, Social experiences, Equilibration.
• Maturation: One of the most important influences on the way we make sense of the world is maturation, the unfolding of the biological changes that are genetically programmed. Parents and teachers have little impact on this aspect of cognitive development, except to be sure that children get the nourishment and care they need to be healthy.
• Hence we conclude that Maturation is the stage in which an individual unfolds his biological changes that are genetically programmed.

Important Points

• ​Piaget identified four factors that influence the development of a child-
• Maturation- Child growing up and biological processes change the thinking pattern.
• Activity- Children tend to act on the environment as they explore, test, and observe.
• Social experiences- Children learn from others through transmission.
• Equilibration-  The tendency to search for balance between the basic tendencies in thinking.
• Adaptation: Adaptation is one schema that describes how people learn and understand new information. 
• ​Example: a child seeing a dog and learning what it is.

Jean Piaget made a systematic study of cognitive development among children of different age groups and he categorized it into different developmental stages. He is also known as the father of child Psychology. According to him, development is based on the physical environment or Biological abilities, he ignores social aspects.

According to him stages of the cognitive development are-

• Sensory-motor:(birth to 2 years)
• Preoperational: (from age 2 years to 7 years)
• Concrete operational:(from 7 years to 11 years)
• Formal operational: (from11+ - adolescence and adulthood).

Key PointsConcrete Operational Stage:

• 'Concrete Operational Stage' lasts around 7 to 11 years of age which refers to the later childhood stage of child development.
• In this stage, children can classify objects into groups and subgroups and gain the ability to conserve numbers, area, and volume.
• Children show attainment of the operations/concepts of reversibility, seriation, and transitivity as a cognitive capacity.
• Adaption ability is not gained by the child at this stage.
• Reversibility is the understanding that a child develops to know that things that have been changed can be returned to their original state.
• Children can conserve numbers (age 6), mass (age 7), and weight (age 9). Conservation is the understanding that something stays the same in quantity even when its appearance changes.
• hence by all these references, we can say that a child can get logic of the operations but not abstraction in the concrete operational stage.​

Important Points

Thinking is the basis of all cognitive activities or processes and is unique to human beings. It involves the manipulation and analysis of information received from the environment. There are different kinds of thinking styles which include creative, logical, concrete thinking, etc.

Key Points A learner can gain thinking capacities by:

• Having engagement in various and different tasks.
• Engaging himself in problem-solving activities.
• Talking aloud to himself also helps children to think and recall the learned concept.
• Group discussion, teamwork, and interaction with society make children's thoughts divergent.
• Thus it is clear that thinking is regulated by talking aloud to the children.

Hint 

• Talking aloud is not an indication of egocentrism.
• Talking aloud enhances psychological and language development.

Lev Vygotsky is a Russian Psychologist who proposed the theory of Socio-cultural development. In this theory, Vygotsky emphasizes the role of society and culture in the development of the child. 

Key Points According to Lev Vygotsky, Cultural tools and Social interaction facilitate the cognitive development of children.

Cultural tools:

• Lev Vygotsky's social-cultural perspective of learning emphasizes the importance of cultural tools in the process of cognitive development.
• Cultural tools are the main determinant of cognitive development and learning. They play a significant role in human intellectual development and how humans perceive the world.
• Learning takes place through the interaction between the child and the culture. Different cultures play a vital role in shaping the abilities and behaviors of a child and work as a tool of intellectual adaptation.​  
• Example: Maps, Language, traditions, calculators, books, and media, are the basic source of cultural tools.

Hence, cultural tools such as maps, language, and calculators aid and change our functioning as per Lev Vygotsky's theory.​

Important Points

 Vygotsky also proposed three basic needs of students during learning, these are Zone of proximal development (ZPD), Scaffolding, and Making knowledgeable others (MKO).

• Zone of Proximal Development (ZPD): The concept of MKO is closely related to ZPD. According to Vygotsky, ZPD is the difference between the present level of development attained without anyone’s assistance and the potential level of development that can be attained under the guidance of MKO.
• Scaffolding: Scaffolding is the term, given by Vygotsky, in which he proposed that the temporary help given by the teachers, family, friends, etc. to the children in his learning.
• MKO (more knowledgeable others): Vygotsky defined the “More Knowledgeable Other” (MKO) as anyone who has a better understanding or a higher ability level than the learner, particularly in regards to a specific task, concept, or process. MKO could be teachers, parents, tutors, and even peers.

Lev Vygotsky is a Russian Psychologist who proposed the theory of Socio-cultural development. In this theory, Vygotsky emphasizes the role of society and culture in the development of the child.

Key Points

• According to Vygotsky, there are three main factors that affect the learning of the child and these are- Social interaction, Culture, and Language:
• Social interaction: ​​Children try to interact with people.
• Culture: ​Children adopt the culture by interaction.
• Language: Children can easily intimate their primary language through interaction or communication.
• Cooperative learning is a synchronized process in which students attempt to learn something together. They work as a team which develops the team spirit and feeling of collaboration. Cooperative learning is done by also social interaction which is proposed by Vygotsky.

Hence we can conclude that rewards and punishment are not a principle of Lev Vygotsky.

Hint

• Operant conditioning:- B.F Skinner propounded this theory as a way of learning by means of rewards and punishments.
• It is a method of learning that employs rewards and punishments for behavior.
• This type of conditioning holds that certain behavior and a consequence, either a reward or punishment, have a connection that brings about learning.

Important Points Four Principles of Vygotsky:

• Children construct their own knowledge: It is rightly said that knowledge is not transferred passively, but is personally constructed by the individual. It means that for the transfer of knowledge, some medium is necessary on the basis of which knowledge can be received but every individual has his/her own way of perceiving the things and as per his/her perception or understanding, he/she constructs his/her knowledge
• Acquisition of knowledge cannot take place without social context: It is correct to say that knowledge cannot be acquired without social context as a human being is a social being and he/she lives in society by following certain rules, and norms of the society, and learn or expand his/her knowledge by interacting with the social surroundings.
• Learning is mediated: Mediated learning takes place when there is an interaction between a learner and a person who is more knowledgeable and helps the learners to modify stimuli and change their own cognitive structure. The person can be a parent, adult, grandparent, or peer and is called by Vygotsky a More Knowledgeable Other (MKO).
• Language plays a central role in cognitive development: Language is the means of communication and socialization. With the passage of time, it becomes a tool for cognitive development or thinking.

Learner or child-centered approach to education means planning and transacting curriculum in the classroom in a way that allows for flexibility in pace and style of learning to keep in mind that children in a classroom are widely different. It, therefore, suggests an approach to teaching different from the existing practice of having a uniform curriculum, uniform learning material and activities, uniform time, and uniform instructional and evaluation strategies for the whole class.

Key Points The environment of the classroom according to the child-centered approach:

• The child and not the teacher is the focus of the entire process of teaching-learning.
• The child is not a passive but an active participant in the classroom process.
• Has a democratic climate so that the child gets maximum opportunities for interaction with other children in the class, with the teacher, and with a variety of teaching-learning material.
• The seating arrangement of the classroom is changed or decided as per the activity of the learners.
• Teacher adopts a variety of teaching-learning strategies to address the needs of all children at the same time.
• The curriculum and the instructional materials serve as a means to foster the child’s all-round development and are not ends in themselves.
• Evaluation of the child’s attainment is done to ensure the child’s progress and not as a means of passing judgment on the child’s abilities and achievement. it is diagnostic as well as remedial.
• **Thus we can consider that children are the center of a child-centered classroom and curriculum and activities are decided as per the child's needs and interest, so that answer written on a blackboard with a reading book in the classroom shows children are the passive learners which are not correct in the context of the child-centered classroom.**​

Important PointsChild-centered approach advocates:

• flexible curriculum
• varied methods of teaching
• varied learning experiences/tasks/activities
• varied learning time
• varied methods of assessing children’s progress.

The gradual formation of an individual's concepts of right and wrong, conscience, ethical and religious values, social attitudes, and behavior is called moral development.​ The theory of a child's moral development is proposed by Lawrence Kohlberg in 1958. he describes the theory on 3 different levels and these 3 levels are further classified into 6 stages.

Key Points

• Stage 5:- The Law and Order Orientation: There is an orientation towards authority, fixed rules, and maintenance of social order. Right behavior consists of doing one's duty, showing respect for established or lawful authority, and maintaining given social order for its own sake. This is a stage of social law and order maintenance proposed by Lawrence Kohlberg.
• In this stage duty is the priority.
• Everyone has personal duty for lawful authority.
• Social order and right behavior is the main feature of this stage.
• Hence we consider that In the stage of social order maintaining, everyone has their own duty to uphold the law.

Important Points

• Stage-I: The Punishment and Obedience Orientation: The physical consequences of an action determine whether the action is good or bad regardless of the human value or the meaning of these consequences. Avoidance of punishment and deference to power are valued in their own right, not in terms of respect for the underlying moral order.
• Stage-2: Instrumental Relativist Orientation: Right action consists of that which instrumentally satisfies one's own needs and occasionally the needs of others.
• Stage 3: Good boy - Nice Girl Orientation: Good behavior is that which pleases or helps others and is approved by them. Behavior at this stage is frequently judged by intentions - "he means well", becomes important for the first time. One earns approval by being good to others.
• Stage 5: The Social Contract, Legalistic Orientation:  in terms of general individual rights and standards that have been critically examined and agreed upon by the whole society. Apart from what is constitutional and democratically agreed upon the right is a matter of personal values. The result is based upon a legal point of view but with a Right to Education emphasis upon the possibility of changing the law in terms of consideration of social utility.
• Stage 6: The Universal Ethical Principle Orientation: Right is defined by the decision of the conscience in accordance with self-chosen ethical principles appealing to logical comprehensiveness, universality, and consistency. These are universal principles of justice, reciprocity, quality of human rights, and respect for the dignity of human beings as individual persons.

Howard Gardner proposed a theory of multiple intelligence. Gardner defines intelligence as "a biopsychological potential to process information that can be activated in a cultural setting to solve problems or create products that are of value in a culture.

Key Points Howard Gardner's theory of multiple intelligences proposes that people are not born with all of the intelligence they will ever have. It includes eight types of intelligence.

• Linguistic intelligence
• Logical-Mathematical intelligence
• Musical intelligence
• Bodily-kinaesthetic intelligence
• Interpersonal intelligence
• Intrapersonal intelligence
• Spatial intelligence
• Naturalistic intelligence

Thus, we consider that Howard Gardner proposes several distant types of intelligence.

Important Points

• Linguistic Intelligence refers to the ability to use language. It is the capacity to use spoken and written words in a skilled way. Individuals with high verbal/linguistic intelligence are very good at using words and language to express themselves, articulate things, and create.
• Logical-mathematical intelligence is the ability to use logical reasoning and mathematical ability. Individuals high in this intelligence have good abstract reasoning, critical thinking, and good in dealing with numbers. This type of intelligence correlates well with the traditional notion of intelligence. Scientists, engineers, physicists, and economists are people with high logical-mathematical intelligence.
• Musical Intelligence is the ability to use rhythms, sounds, and patterns to create, compose and perform music. It involves sensitivity to music, and the ability to recognize and manipulate musical patterns. People with high musical intelligence are likely to be singers.
• Bodily-kinesthetic intelligence is the ability to use and control one’s body movements and actions. Dancers and sports persons are usually high in such intelligence.
• Spatial Intelligence is the capacity to perceive, understand and use spatial and visual information effectively. Such people are good at spatial orientation, forming visual images and patterns.
• Interpersonal Intelligence refers to the ability to understand others and social interactions. They can understand the emotions and the perspectives of others and relate well to others. They can establish good interpersonal relationships with others. They have good and effective communication skills.
• Intrapersonal Intelligence is the ability to understand oneself and know one’s thoughts, emotions, feelings, motives, and desires, and how these influence their behavior.
• Naturalistic Intelligence is the ability to recognize and understand the various patterns in nature. It includes sensitivity to nature with all its features including flora, fauna, and biodiversity. Gardner has added this eighth type of intelligence to his original seven bits of intelligence.

Gender refers to the socially constructed differences between men and women. It refers to the masculine and feminine qualities, behavior, roles, and responsibilities that society upholds. Gender can be changed / re-oriented.

• A stereotype is a simplified and/or standardized conception or image with specific meaning, often held in common by people about another group. A stereotype can be a conventional and oversimplified conception, opinion, or image, based on the assumption that there are attributes that members of the other group hold in common.
• Gender stereotype is an oversimplified and unfair belief or idea that groups of people have particular characteristics or that all people in a group are the same.

Key Points Gender stereotyping can be challenged by following these ways:

• Treating the girls and the boys equally.
• Gave the same and equal opportunity to all the students without making any difference between them.
• Promoting discussions about gender as a social construct.
• Promoting flexibility in the classroom.
• Flexibility in language always uses gender-neutral languages.
• Presenting Non-stereotypical sex roles, such as a girl riding the bike, or a boy cooking in a kitchen.
• Gender should not be biologically defined.
• Engagement of every student in all the activities without distinguishing them.
• The sitting arrangement of all the boys and girls should not be separated.

So by all these references, we can conclude that use of gender neutral language and discussing gender as a social construct rather than being biologically determined would **challenge gender stereotyping.**​

Hint

• Gender Bias: Gender bias results when one gender is treated less favorably than the other, often referred to as sexism and it has a range of consequences including being Scientifically misleading. Upholding stereotypical assumptions. Validating sex discrimination.

Inclusive education ensures that children with special needs are taught in regular schools with their age and grade peers with support services provided within the school system. Thus, it reflects the objective of providing quality education to all children by accommodating their needs and learning styles into the general curriculum.

Key Points In an inclusive classroom, there are many learners having different abilities, cultures, physical and mental health, and disabilities. So a teacher should follow:

• Equitable education for all, including challenging, backward, disabled children.
• using diverse pedagogical/instructional strategies and respecting individual students’ pace of learning.
• All the students of different abilities, differences, and disabilities are treated equally.
• Inclusive education provides barrier-free access for all students.
• Creating an environment in which the child can learn with diversity, not creating a special environment for learning.
• Emphasis on their learning to read instead of emphasizing teaching.
• providing choice and options for learners amidst an array of activities and experiences.
• Thus we can consider that different instructional styles facilitate the learning of the students in diverse classrooms.

Additional Information In Inclusive education the main objectives are- 

• flexibility in learning.
• Creating an environment in which the child can learn with diversity, not creating a special environment for learning.
• Equitable education for all, including challenging children.
• Emphasis on their learning to read instead of emphasizing teaching.
• To use different teaching methods according to the needs of each student, so that every child can have access to the knowledge.

Assessment refers to the collection of data and the gathering of evidence from different sources through different tools. An assessment provides feedback on the performance of the student specifying his/ her strengths and areas for improvement which provides insights for taking appropriate steps for improving the learning.

Key Points Characteristics of Assessment:​

• Stimulates continuous evaluation, not just term-end evaluation.
• Gives immediate and constructive feedback.
• Ensures all-around development of all the learners, not just special children.
• Complements traditional external examination.
• Uses assessment tools designed by school teachers.
• Emphasizes both scholastic and co-scholastic aspects of growth.
• Integrate teaching learning and assessment
• No-load on teachers' documentation, recording, reports
• Child-centered and activity-based pedagogy
• Focus on competency development rather than content memorization
• Broadening the scope of assessment by way of including self-assessment, and peer assessment besides teacher assessment.
• Assessment is also a part of the teaching-learning process.
• Nonthreatening stress-free and enhanced  participation/interaction
• Focus on assessment of/and/as learning rather than the evaluation of achievement
• By all these references we can consider that Assessment is not separated from the teaching-learning process. It is a part of teaching-learning process.

Additional Information Basically there is three types of assessments:

• Assessment of learning
• Assessment for learning.
• Assessment as learning

Inclusive education is an approach to educating all children who are at risk for neglect in the education system. It expects that all learners learn together through access to common educational provisions. The crucial people in the system are the parents, community, teachers, administrators, and policymakers. All these people have to be supportive of the diverse needs of children.

Key Points In Inclusive education the main objectives are-

• All the students of different abilities, differences, and disabilities are treated equally.
• Inclusive education provides barrier-free access for all students.
• Creating an environment in which the child can learn with diversity, not creating a special environment for learning.
• Equitable education for all, including challenging children.
• Emphasis on their learning to read instead of emphasizing teaching.
• Emphasis on their learning to read instead of emphasizing teaching.
• To use different teaching methods according to the needs of each student, so that every child can have access to the knowledge.
• Equitable education for all, including challenging, backward, disabled children.

So by all these references, we can conclude that inclusion in education implies that all the children are learning under the same roof without their diffrences.

Hint

• All types of students are comes under the concept of inclusive education there is no selection process on the basis of their ability for the inclusive classroom.
• Adjustment is not on demand by the students, all types of learners learn so adjustment is the main feature of inclusive education.
• All type of students learns under the same roof in the inclusive classroom, either a student of special needs or multi-talented students.

Learning Disability: It is a neurological disorder that prevents a person from learning a skill and using it effectively. Generally, it occurs in childhood and is characterized by difficulty with certain skills such as reading, writing, speaking, etc.

Key Points Dyslexia: It is a Reading disability, which is not due to mental retardation, brain damage, or a lack of intelligence. It is caused by an impairment in the brain’s ability to translate images received from the eyes or ears into understandable language. Characteristics of the learners with Dyslexia:

• They are unable to correct the letters if reverse letters are provided to them.
• Read the words oppositely.
• Unable to recognize mirror images of the letters.
• They are unable to recognize words, and spelling and can not decode the letters.
• They face challenges in reading and comprehending the written materials.
• Students found confusing while reading, they are unable to figure out the correct letter.
• Reading wrong due to lack of understanding of the words and letters.

Thus we can consider that Dyslexia is a reading disability, in which a learner faces problems related to reading and comprehending the written materials.

Important Points

• Hearing impairment: "hearing impairment" means loss of sixty decibels or more in the better ear in the conversational range of frequencies.
• Locomotor Disabilities: "locomotor disability" means disability of the bones, joints, or muscles leading to substantial restriction of the movement of the limbs or any form of cerebral palsy.
• Dyscalculia is a disability resulting in difficulties such as difficulty in understanding numbers, learning or comprehending arithmetic, learning how to manipulate numbers, performing mathematical calculations, and learning facts in mathematics.

Inclusive education goes beyond children with disabilities and refers to an education system that accommodates all children regardless of their physical, intellectual, social, emotional, linguistic, or other conditions. 

Key PointsDECONTEXTUALIZATION is the Process of examining or interpreting something that is separate from the context in which it is embedded. "Decontextualization occurs consciously or subconsciously." The content and curriculum should be designed according to the laid principles of inclusive education,

In Inclusive education the main objectives are- 

• flexibility in learning.
• Creating an environment in which the child can learn with diversity, not creating a special environment for learning.
• The child is the center of the classroom, classrooms should be child-centered.
• Equitable education for all, including challenging children.
• Respects all the traditions and cultural backgrounds from which the students belong.
• Assessment and evaluation of the students cover all the aspects, it should not only pen-paper exam.
• Emphasis on their learning to read instead of emphasizing teaching.
• Contextualized content is a part of the teaching-learning process in inclusive education, delivering the right concepts at right time to the students is one of the important features of inclusive education.
• To use different teaching methods according to the needs of each student, so that every child can have access to the knowledge.
• Hence we can conclude that Decontecxtualized content is not a part of inclusive education.

Important Points Basic Principles of Inclusive Education:

• Well constructed educational plan.
• Use of multilingualism as a resource.
• Equity and equal opportunities for all.
• Use of specific pedagogical strategies.
• Sensitization towards individual differences.

Inclusive Education is a new approach toward educating children with disabilities and learning difficulties with those normal ones under the same roof. It seeks to maximize the potential of all students.

• Inclusive Education mainly refers to the inclusion of all children in the education system, regardless of their differences and disabilities.
• It values the diversity, each child brings to the classroom and facilitates all equal opportunities to learn and grow.

Key PointsCharacteristics of inclusion of students in inclusive education:

• All types of students such as those having learning disabilities, physical impairment, and biological problems, are mentally retired, creative, active, and intelligent. etc. learns under the same roof.
• Different Pedagogical techniques should be used as per the need of individual and their capacity.
• Flexibility in the curriculum.
• Classrooms are child-centered instead of teacher-centered.
• Various learning techniques/methods should be used as per the need and interests of the learners on an individual basis.
• Hence we can say that Teachers should cater to the students with different skills, abilities, and disabilities by using different pedagogical techniques.

Important Points Basic Principles of Inclusive Education:

• Well constructed educational plan.
• Use of multilingualism as a resource.
• Equity and equal opportunities for all.
• Use of specific pedagogical strategies.
• Sensitization towards individual differences.

The term "Disability" is, generally speaking, a kind of absence or lack of one or more capacities that the majority of human beings possess and without which our physical or mental activities are restricted partially or totally. 

‘Locomotor Disability’ refers to a person’s inability to execute distinctive activities associated with the movement of self and manipulation of objects resulting from affliction of the musculoskeletal and/or nervous system.

Key Points

• It is related to the disability of bones, joints, and muscles thus causing problems that may be partial or complete to performing normal functions/activities which a human being is normally able to do like talking, walking, hearing, seeing, and so on.
• It also makes the child unable to grasp an object and to raise both arms without any difficulties.
• Disability of the bones, joints, or muscles leads to substantial restriction of the movement of the limbs or a usual form of cerebral palsy.
• Some common conditions giving raise to locomotor disability could be poliomyelitis, cerebral palsy, amputation, injuries to the spine, head, soft tissues, fractures, muscular dystrophies, etc.

Hence we can say that Provision of classes on the ground floor is important for the learners who suffer from locomotor disabilities. 

Important Points Some common conditions that can cause locomotor disability are

• Soft Tissues
• Muscular Dystrophies
• Dwarfism
• Spinal Injuries
• Injuries of Head
• Amputation
• Fractures

Hint

• Dysgraphia: Dysgraphia is a disability in which student faces difficulties related to writing, they can not write properly.
• Dyslexia: It is a Reading disability, which is not due to mental retardation, brain damage, or a lack of intelligence. It is caused by an impairment in the brain’s ability to translate images received from the eyes or ears into understandable language.
• The term 'visual impairment' is used to refer to not only those who are blind but also those who have low vision. In the teaching-learning process,  visually impaired children suffer from an issue with sight or vision but when they are facilitated with the right training and tools, they develop a good literacy ability.

Thinking is the basis of all cognitive activities or processes and is unique to human beings. It involves the manipulation and analysis of information received from the environment. There are different kinds of thinking styles which include creative, logical, concrete thinking, etc.

Key Points A learner can gain thinking capacities by:

• Having engagement in various and different tasks.
• Engaging himself in problem-solving activities.
• Creative work such as model making improves thinking power and also makes the learners think divergent.
• Talking aloud to himself also helps children to think and recall the learned concept.
• Group discussion, Peer discussion, teamwork, and interaction with society make children's thoughts divergent.
• Hence we can say that Discussion with peers is a way to facilitate students' thinking because during discussion students can learn from the views of their peers.

Hint

• Drilling is a method of instruction that involves systematic repetition of concepts, examples, and practice problems.
• Copying without understanding can not emphasize the thinking of the students, because without understanding a learner can not get the concept of a related problem.
• Passive listening, however, is like listening while multitasking.
• A passive listener might pay attention to a speaker with the sole intent to respond or place some of their attention on another task.

Listening : It means when you listen to someone or pay attention to what she is saying. There are two types of listening: 

• Active listening
• Passive listening

Key Points Effective of passive listening on the learning of the students:

• Reduced work performance.
• leaves a bad impression on students.
• they might miss out on important information.
• they might are not able to listen properly.
• As a teacher, you must avoid passive listening for students because students learn and enjoy interactive learning. in passive learning, they will get bored and will not listen.

Hence, it is important to avoid situations where the students are passive listeners for long periods.

Hint

• If we create situations that make students passive listeners for a longer period they will not pay attention and miss out on the important things.
• If we prevent the students from being active learners they will not catch up on things easily and they will get bored.

Important Points

 Active listening: It means to listen to someone carefully and pay full attention or focus on them. it includes the feedback and it is two-sided communication.​ Some suitable situations for active listening:

• the telling story in front of the class.
• reciting poems with the class.

Passive Listening: It means listening without asking questions or interrupting the speaker. It is typically one-sided communication with no or very less feedback.

Some suitable situations for passive listening:

• listening to music while working.
• watching television while checking emails.

Additional Information  Interactive learning: In this type of learning learner is equally involved and provides proper feedback. 

• Examples: quiz, story formation, etc.

Learning is a continuous life-long process that is not inherited but can begin right from birth by providing constant interaction and stimulation received from the physical, social, and cultural environment and it does not stop till the end.

Meaningful learning: Meaningful learning results when a person consciously and explicitly ties new knowledge to relevant concepts they already possess. When meaningful learning occurs, it produces a series of changes within our entire cognitive structure, modifying existing concepts and forming new linkages between concepts.

Key PointsCharacteristics of Learning in a meaningful way:

• It stresses the ability of the learner to apply what is learned because of the involvement of the learners.
• Meaningful learning is possible only when learners make a deliberate effort to relate new knowledge to the relevant concept they already know.
• It is the active creation of knowledge structures from personal experience.
• This type of learning encourages students to ask questions and the logic behind the concepts.
• Different types of meaningful activities are organized to learn conceptually and make the best understanding of the concept.
• Students have been involved directly so meaningful learning is a child-centered method of teaching in which the teacher feels the interest and values of the students.
• Meaningful learning is the human mechanism par excellence for acquiring and storing a vast quantity of ideas.
• Hence by all these references, we can conclude that learning should be best, effective, and understandable if it will be done in a meaningful manner.

Hint 

• Learning should be done by covering all the factors it should not be based on a single factor such as society, culture, tradition, etc.

Learning is a continuous life-long process that is not inherited but can begin right from birth by providing constant interaction and stimulation received from the physical, social, and cultural environment and it does not stop till the end.

Key Points There are some following ways that should be followed by teachers to encourage students:

• The classroom environment should be flexible.
• No rigidity in the rules and instructions of the teachers.
• Teachers should not mediate in the learning of the students.
• Rules and instructions should be designed as per the needs of the students and which can help the students.
• Facilitating collaborative learning.
• Teachers should ensure that the rules and instructions are not confusing and discourage the students.
• Provide equal opportunities to all the students so that they can feel as if they all are treated equally by the teacher.

Thus by all these references, we can say that rigidity in rules and instruction can discourage the students so teachers should have to make rules and regulations flexible.

Hint

• Scaffolding : It is a help given by teacher to the students for effectiveness of task and teaching them how to learn and do that particular task on their own.
• Transfer of learning: It refers to the influence of learning one task on the learning of another.

Additional Information  The teacher should not design the instruction that confuse or discourage the students that will lead students to: 

• Demotivation
• Confusion
• Not liking the teacher
• Says no to school

Constructivism is centered on the idea that human knowledge and learning are actively constructed by the learner, not passively received from the environment.

Social constructivism is founded on the thesis that social processes are central to learning and cognitive development. It regards knowledge as a social construct and prioritizes the social aspects of learning and cognitive development. Some of these social aspects are language, culture, everyday practices, material objects, interpersonal interaction, peer interaction, tools, and symbols.

Key Points The factor that promotes socio constructivism are:

• Lev Vygotsky explains the role of society in the socio-constructivist approach to learning:
• Social interaction- Society plays an important role in the development and knowledge gained by the child.
• Culture - culture plays an important role in the development of a child, a child behaves as same as they learn from their culture, society, and environment.
• Scaffolding: Scaffolding is the term, given by Vygotsky, in which he proposed that the temporary help given by the teachers, family, friends, etc. to the children in his learning.
• Discovery learning is a technique of inquiry-based learning and is considered a constructivist based approach to education. Discovery-based learning is typically characterized by having minimal teacher guidance, fewer teacher explanations, solving problems with multiple solutions, use of hand-on materials, minimal repetition, and memorization.
• **Hence we can say that culture, scaffolding, and discovery learning promote socio constructivism.**​

Hint

• Conditioning of behavior: This method does not depend on the involvement of the society in the learning of the learner, this type of learning depends on conditions and changes in behaviour by cognition.

Problem-solving skills: It is a skill by which students try to find their solutions to different problems. Problem-solving skills are those that allow you to identify and understand the causes of a problem, then solve it.

 Key Points To enhance problem-solving skills of the students a teacher should do the following :

• Provide help to the students but not the proper solution to the problem, so they can learn by using their cognitive skills.
• Create situations that demand the application of knowledge.
• engage them in different types of problems so that they can solve the problem by using their divergent thinking and observation skills.
• Allow students time to find their way to solve the respected problem.
• Ask questions to the learners and keep interacting with them.
• Provide encouragement and appreciation.

Hence, To enhance the problem-solving skills of students, create situations that demand the application of knowledge is a good strategy.

Important Points A teacher should not promote these methods of learning in the classroom:

• Rote-memorization: It does not help the students to learn conceptually, this is just memorization-based learning.
• Copy from the board: This is not a meaningful way of learning, learners can not learn meaningfully by these type of methods.

Misconceptions refer to a wrong or inaccurate idea that takes place due to the mismatch in previously assimilated and the newly accommodated knowledge. 

• misconceptions in students' life are playing important role in the teaching-learning process. They are necessary for the learning process to give insight into students' thinking.

Key Points Views of teachers towards misconceptions should:

• Teachers should not ignore students' misconceptions rather they should identify misconceptions and try to clear them by examples, various methods of teaching, etc.
• Use various techniques such as discovery learning, which helps students to identify and correct their misconceptions.
• The teacher should have to provide opportunities related to the concepts so that student can understand their mistakes point and can fix them.
• Summative assignments that ask students to explain their reasoning are useful for detecting students' misconceptions.
• Teachers should provide a forum for students to confront their misconceptions and should help students reconstruct and internalize their knowledge.
• Hence by all these references, we can conclude that providing opportunities related to the concepts can counter the misconceptions.

Hint

• The teacher should not have to punish the students on misconceptions, because it is part of the teaching-learning process, and a teacher should have to use different pedagogical techniques to the students so that they can fix their mistakes in concepts.
• Direct involvement of the students having misconceptions in the remedial teaching is not a relevant method.

Learning is a continuous life-long process that is not inherited but can begin right from birth by providing constant interaction and stimulation received from the physical, social, and cultural environment and it does not stop till the end.

Key Points Learning process can be improved by:

• Involvement in tasks without fear of failure.
• Students' learning can be improved by asking questions where they needed without shame.
• Engagement in different social activities, team works, group discussions, etc.
• The environment should not be fearful.
• Students should not perform shameful behavior during the teaching-learning process, it can harm their learning and also can decrease their understanding level.
• The student should have to think divergently and learn through discovery to improve the learning process.
• **Hence, we can consider that shame can harm the learning process of the students.**​

Important PointsThere are many emotions that facilitate the process of learning in a meaningful way, these are-

• ​Happiness
• Hope
• Pride
• Curiosity
• Enjoyment.

National Education Policy 2020-

According to NEP 2020, A good educational institution is one in which every student feels welcomed and cared for, where a safe and stimulating learning environment exists, where a wide range of learning experiences are offered, and where good physical infrastructure and appropriate resources conducive to learning are available to all students.

Key Points

Some important fundamental principles of the NEP 2020 are- 

• Full equity and inclusion as the cornerstone of all educational decisions to ensure that all students are able to thrive in the education system.
• It includes the overall development of the leader, it covers all three aspects as Cognitive domain, affective domain, and psychomotor domain.
• Emphasis on conceptual understanding rather than rote learning and learning-for-exams.
• Promoting self-assessment and the peer assessment done by the student in the classroom.
• Assessment of the students should be in a formative way instead of a summative assessment,
• Respect for diversity and respect for the local context in all curricula.
• The curriculum becomes flexible as per the needs and interests of the students.
• pedagogy, and policy, always keeping in mind that education is a concurrent subject.
• Establishment of the linkage of the concepts with the environment or we can say that the linkage of the school with the home.
• Promoting multilingualism and the power of language in teaching and learning.
• Creativity and critical thinking encourage logical decision-making and innovation.
• It emphasizes group work as well as individual work, NEP 2020 links the study to the curriculum.
• Hence we can say that in NEP 2020, the standardization of the curriculum is eliminated and promotes flexibility.

Learning is a continuous life-long process that is not inherited but can begin right from birth by providing constant interaction and stimulation received from the physical, social, and cultural environment and it does not stop till the end.

Key Points

• Learning should have to be based on understanding.
• Teachers should always teach in a conceptual manner.
• Learning should be in a meaningful way.
• Rote learning or learning through memorization should not be promoted by the teachers it makes a negative impact on the learning process of the students.
• So that learning should be much effective when it is directed toward understanding rather than memorization.

Hint 

• Rote memorization is defined as memorization by repetition, often without an understanding of the reasoning or relationships involved in the material that is learned.

Additional Information

• Behavioristic learning: Behavioristic theories or Behaviorism constitute the traditional theories of Learning. These theories were propounded by Ivan Pavlov and John B. Watson. The behaviorists attribute learning to the association between stimulus and response. Behavioristic theories are also called the connectionist theories of learning because of their emphasis on the connection between the stimulus and the response. They mainly deal with the role played by conditioning in the process of learning.
• Discovery learning: Discovery learning is the type of learning in which students can learn by finding the correct approach for the problem through their cognition.
• Humanistic learning: This is a learning in which learning totally depends on the interest, needs, and abilities of the child, it is also called student-centered learning. Students are encouraged to learn in this type of learning.

Given:

x = $-\frac {2}{3}$ and y = $-\frac 3 4$,

Calculation:

⇒ x = - (2/3) and y = -(3/4)

⇒ x^-1 = (1/x) = -(3/2) and y^-1 = (1/y) = -(4/3)

Now,

⇒ (x-1 + y-1) = ((-(3/2)) + (-(4/3)) = ((-3/2) - (4/3))

⇒ LCM of 2 and 3 is 6

⇒ So, (x-1 + y-1) = ((-9/6) - (8/6)) = -(17/6)

The Reciprocal of (x-1 + y-1) = 1/(x-1 + y-1) = -(6/17)

Calculation:

To solve this question we have to check all the options:

Option 1): √0.9 = 0.3

Now, The value of √(0.9) = √(9/10) = 3√(1/10) which is not equal to 0.3, the this option is false.

Option 2): For an integer, a, a3 is always greater than a2.

An integer is defined as a number that can be written without a fractional component. 

⇒ False. Hence, -2² is greater than -2³

Option 3) If a2 ends in 9, then a3 ends in 7.

⇒ a³ ends in 7 if "a" ends in 3, but for every a² ending in 9, it is not necessary that "a" is 3.

If a = 7 then a² = 9 but a³ ≠ 7

So, it is False.

Option 4) If a divides b, then a3 divides b3.

⇒ If a divides b then b must be a multiple of a, so a³ will divide b³.

⇒ It is a true statement.

Given:

$[(\frac{4}{3})^2]^3 \times (\frac{2}{3})^{-4} \times (\frac{27}{16})^2 \div 3^3$

Formula used:

(a^m)ⁿ = a^m×n

(a/b)^-n = (b/a)ⁿ

a^m × aⁿ = a^m+n

Calculation:

$[(\frac{4}{3})^2]^3 \times (\frac{2}{3})^{-4} \times (\frac{27}{16})^2 \div 3^3$

⇒ $(\frac{4}{3})^6 \times (\frac{3}{2})^4 \times (\frac{3^3}{2^4})^2 \times \frac{1}{3^3}$

⇒ $\frac{(2^2)^6}{3^6} \times \frac{3^4}{2^4} \times \frac{3^6}{2^8} \times \frac{1}{3^3}$

⇒ $\frac{2^{12} \times 3^{4+6}}{3^6 \times 2^{4+8} \times 3^3}$

⇒ $\frac{2^{12} \times 3^{10}}{2^{12} \times 3^9}$

⇒ 3^10-9

⇒ 3

∴ The correct answer is option (1).

Solution:

Let x be added 

Now, A/Q

(0.102 + 0.25 + 0.111 + 0.1) + x = 1

⇒ 0.563 + x = 1

⇒ x = 1 - 0.563

⇒ 0.437

Given:

x = 25 × 32 × 53,

y = 24 × 33 × 52 

z = 23 × 33 × 52

Concept:

LCM is the product of the maximum number of each prime factor that occurs in either of the numbers.

HCF is the product of the lowest powers of each of the prime factors that commonly occurs in both the number.

Calculation:

x = 25 × 32 × 53,

y = 24 × 33 × 52 

z = 23 × 33 × 52 

⇒ HCF = 2³ ×  3² × 5²

⇒ LCM = 25 × 33 × 53 

Now, (LCM of x, y and z) ÷ (HCF of x, y and z) = 

⇒ (25 × 33 × 53)/(23 ×  32 × 52) = ( 22 × 3 × 5) = 4 × 15 = 60

Given:

The area of the square field = 256 m²

The width of the rectangular lawn = 5/8 of the side of the square field.

The perimeter of the square field and the rectangular lawn is the same.

Concept:

The area of square = a²

The perimeter of square = 4a

The area of rectangle = length × breadth

The perimeter of rectangle = 2(length + breadth)

Calculation:

The area of square field = a2 = 256 m2

So, the side a of the square field = 16 m

Now the width of rectangular field =  5/8 of the side of square field

The width of rectangular field = 5/8 × 16 = 10 m

Now the perimeter of square field = 4a = 4 × 16 = 64, which is equal to the perimeter of rectangular field.

So, perimeter of rectangular field = 2(length + 10) = 64,

Length of rectangular lawn = 22 m

Area of rectangular lawn = 22 × 10 = 220 m²

Given:

The volume of the tank = 352 m³

The diameter of the base = 8 m

so, the radius of the base = 4 m

Concept:

The volume of the cylinder = πr²h

Calculation:

The volume of cylindrical tank = πr2h = 352 m3

⇒ πr2h = 352 m3  

⇒ (22/7) × 42× h = 352 m3 

⇒ h = 7 m

Given:

x2 - 4x - 21 and x2 + 10x + 21

Calculation:

Finding factors of x2 - 4x - 21

⇒ x2 - 4x - 21 = x2 - 7x + 3x - 21

⇒ x(x - 7) + 3(x - 7)

⇒ (x + 3)(x - 7)

Now finding factors of x2 + 10x + 21

⇒ x2 + 10x + 21= x2 + 7x + 3x + 21 

⇒ x(x + 7) + 3(x + 7)

⇒ (x + 3)(x + 7)

Now, One factor common to x2 - 4x - 21 and x2 + 10x + 21 is (x + 3)

Given:

(x - y + z)² - (x - y - z)²/4

Concept:

(x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yz

Calculation:

Expanding (x - y + z)2 =  x2 + y2 + z2 - 2xy + 2xz - 2yz

Now, Expanding  (x - y - z)2 = (x - y - z)² = x² + y² + z² - 2xy - 2xz + 2yz 

Now, (x - y + z)2 - (x - y - z)2 = (x2 + y2 + z2 - 2xy + 2xz - 2yz) - (x2 + y2 + z2 - 2xy - 2xz + 2yz)

⇒ x2 + y2 + z2 - 2xy + 2xz - 2yz - x2 - y2 - z2 + 2xy + 2xz - 2yz 

⇒ 2xz - 2yz + 2xz - 2yz = 4xz - 4yz = 4z(x - y)

Now, calculating for (x - y + z)2 - (x - y - z)2/4 = 4z(x - y)/4 = z(x - y)

Given:

The sum = ₹20000

Rate of interest = 10% p.a.

Time = 2.5 years.

Concept:

When the interest is compounded annually but rates are different for different years

Let principal = P, time = 2 years, and let the rates of interest be p % p.a. during the first year and q % p.a. during the second year.

<br>

Then, amount after 2 years = {P × (1 + P/100) × (1 + q/100)}.

<br>

This formula may similarly be extended for any number of years.

Calculation:

The rate for first-year = 10%

The rate for the second year = 10%

The rate for the third year = 5% ( because time is half a year)

Now,  amount after 3 years = {P × (1 + P/100) × (1 + Q/100) × ( 1 + R/100)}

⇒ {P × (1 + 10/100) × (1 + 10/100) × ( 1 + 5/100)} = P × (11/10) × (11/10) × (21/20)

⇒ Rs 25410 

Now interest compounded = Rs (25410 - 20000) = Rs 5410

Given:

(4x - 7y) (4x + 7y) - (3x - 2y)2 + (x2 + y2)

Concept:

A coefficient is an integer that is written along with a variable or it is multiplied by the variable.

Calculation:

(4x - 7y) (4x + 7y) - (3x - 2y)2 + (x2 + y2)

Expand this equation by multiplying and opening the square terms:

⇒ (4x - 7y) (4x + 7y) - (3x - 2y)2 + (x2 + y2)

⇒ (4x)² - (7y)² - 9x² - 4y² + 12xy + x2 + y2 

⇒ (16x2 - 49y2 - 9x2 - 4y2 + 12xy + x2 + y2 )

⇒ 8x2 - 52y² + 12xy

Hence, the coefficient for y² is -52

Given:

4 - 1/2(2x + 5) = 2(x - 4)/3

Calculation:

Solving the above equation to find the value of x

⇒ 4 - 1/2(2x + 5) = 2(x - 4)/ 3

⇒ (4 - x - 5/2) × 3 =  2x - 8

⇒ (12 - 3x - 15/2) =  2x - 8

⇒ 5x = 25/2 = 5/2

⇒ x = 5/2

Now finding the value of 4x2 - 5x + 4 by putting the value of x = 5/2

⇒ 4x2 - 5x + 4 = 4(25/4) - 5(5/2) + 4 = 25 - 25/2 + 4 = (50 + 8 - 25)/4

⇒ (58 - 25)/4 = 33/2 = 16$\frac 1 2$

Given:

12, 7, 13, 3, 16, 15, 18, 19, 27, 18, 34, 29

Concept:

Mode = Most repeated term of a data

The range of the data is the difference between the largest value and the smallest value.

If the total number of observation(n) is an odd number,

Median = ((n + 1)/2)^th term

If the total number of observations(n) is an even number,

Median = ((n/2)^th term + ((n/2) + 1)^th term)/2

Mean = (Mode + Range + Median)/3

Calculations:

Arranging the given terms in Ascending order,

3, 7, 12, 13, 15, 16, 18, 18, 19, 27, 29, 34   

Most repeated term = 18 (2 times)

⇒ Mode = 18

Number of terms = 12

Median = ((12/2)^th term + ((12/2) + 1)^th term)/2

⇒ Median = (6^th term + 7^th term)/2

⇒ Median = (16 + 18)/2 = 17

⇒ Range = (34 - 3) = 31

⇒ Mean of the mode, median and range = ( 18 + 17 + 31)/3 = 66/3 = 22

Mean of the mode, median and range = 22

Given:

ABCD is a parallelogram

∠D = 76° and  The bisectors of ∠C and ∠D meet a point O

Calculation:

ABCD is a parallelogram

⇒  ∠C+∠D=180° [ Sum of adjacent angles of parallelogram are supplementary]

⇒ ∠C = 180° - 76° = 104° 

⇒ ∠C/2 = ∠OCD = 52° and ∠D/2 = ∠ODC = 38°

In △COD

⇒  ∠OCD + ∠COD + ∠ODC = 180° 

⇒  52° + 38° + ∠COD = 180° 

⇒ ∠COD = 180° - (52° + 38°)

⇒ ∠COD = 180° - 90° = 90°

Given:

In ∆ABC, D is the mid-point of BC such that AD = BD.

and ∠ADB = 102° .

Calculation:

In Δ ADB,( isoceles triangle as AD = BD)

⇒ ∠BAD + ∠B + ∠ ADB = 180° 

⇒ ∠B + ∠B + 102° = 180° 

 ⇒ ∠B = 78°/2 = 39° = ∠BAD

Since D is the mid point of BC, BD = CD so, CD = AD

⇒ ∠ADC = 180° - 102° = 78° (Straight line)

Now in ΔADC,( isoceles triangle as AD = CD)

⇒ ∠CAD + ∠C + ∠ ADC = 180° 

⇒ ∠C + ∠C + 78° = 180° 

⇒ 2∠C = 180° - 78° =  102° 

⇒ ∠C = 51° 

Now, ∠BAC = ∠DCA + ∠DAB = 51° + 39° = 90°

Given:

x is the angle (in degree) which is 34° less than its supplement 

y is the angle (in degrees) which is 38° more than its complement

Concept:

When the sum of two angles is 90°, then the angles are known as complementary angles

When the sum of two angles is 180°, then the angles are known as supplementary angles.

Calculation;

Supplementary angle of x = (180° - x)

According to the question:

⇒ x = (180° - x) - 34° = (180° - x - 34°

⇒ x = 73° 

Now Complemetry angle of y = (90° - y)

According to the question:

⇒ y =  (90° - y) + 38° = (90° - y + 38°)

⇒ y = 64° 

⇒ (2x - y) = (2(73°) - 64°)) = 82°

Given:

ABCD is the rhombus where AC= x cm and BD= y cm

Calculation:

Let ABCD be the rhombus where, AC= x cm and BD= y cm

Let AC and BD intersect each other at O. Now, diagonals of the rhombus bisect each other at right angles.

Thus, we have

AO = (1/2) × AC = (1/2) ​× x = x/2 cm and 

BO = (1/2) × BD = (1/2) ​× y = y/2 cm

In right angled △AOB,

⇒  (AB)² = (AO)² + (BO)²

⇒  (AB)² = (x/2)² + (y/2)²

⇒  (AB)² = x²/4 + y²/4

⇒ (AB)2 = (x2 + y2)/4

⇒ The length of a side of the rhombus = AB = $\frac 1 2 {\sqrt{{{x^2}+{y^2}}}}$

Given:

F represents the number of faces,

V represents the number of vertices and 

E represents  the number of edges

Concept:

A square-based pyramid has 5 faces (F), 4 equal triangles and a square base.

A square-based pyramid has 8 edges (E).

A square-based pyramid has 5 vertices (V).

Calculation:

Number of faces = F = 5

Number of edges = E = 8

Number of vertices = V = 5

So,(3V + 2F - E)= 3(5) + 2(5) - 8 = 15 + 10 - 8 = 17

Given:

DImensions of cuboidal box = 120 cm × 60 cm × 48 cm

Number of wooden cubes of the same size = 200

Concept:

The Volume of the cuboid = L × B × H

The Volume of the cube = A³

The lateral surface area of the cube = 4A²

Calculation:

Volume of box = 120 cm × 60 cm × 48 cm

Volume of each wooden cubes = (120 cm × 60 cm × 48 cm)/200

 ⇒ A³ = 1728 cm³

⇒ A = 12 cm

Lateral surface area of each cube = 4 × A² = 4 × 122 = 576 cm²

Given:

The number of cards numbered = from 47 to 82.

Concept:

Number of cards = an = a + (n – 1)d 

Probability P(E) =(No. of favorable outcomes)/(Total no. of possible outcomes)​

Calculation:

Let E be the event of getting a prime number in the event of drawing a card numbered 47, 48, 49,...., 81, and 82 from the box

Prime numbers from 47 to 82 = 47, 53, 59, 61, 67, 71, 73, 79,

No. of favorable outcomes = 8

Number of cards = an = a + (n – 1)d = 82 = 47 + ( n -1 )d

⇒ n = 36

⇒ Total no. of possible outcomes = 36

We know that, Probability P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes) ​= 8/36 = 2/9

Therefore, the probability that the number on the card drawn is a prime number is 2/9.

Algebra is a branch of Mathematics where the principles of Arithmetic are generalized by using letter symbols representing numbers.

Key PointsAction research is a process by which change and understanding can be pursued at one time. It is usually described as cyclic, with action and critical reflection taking place in turn. The reflection is used to review the previous action and plan the next one.

• Action Research is a method of systematic inquiry that teachers undertake as researchers of their practice.
• Action researchers recognize that as the research process unfolds, the research problem may evolve, requiring a new definition of the situation as well as new methods of understanding. hence, a teacher observes that class VII learners face difficulties in understanding algebra. The teacher carries out an experiment devising a special method of introducing algebra. by doing so the teacher took action research then, He/she incorporates the finding into his mathematics practice.
• Action research is a useful way of researching if you are a practitioner who wishes to improve your understanding of your practice.
• Its other common use is by activists who wish to engage the clients as coresearchers.
• It can also be used for preliminary or pilot research before using some other research approach - this is less common, but potentially very useful
• Both action research and action learning may be compared to experiential learning. As usually described, as a process of learning from experience.

Therefore, when the teacher carries out an experiment devising a special method of introducing algebra. He/she incorporates the finding into mathematics practice. This is an example of Action Research**.**

Additional Information

• Error analysis is a method used to document the errors that appear in learner procedure, determine whether errors are systematic, and then explain what caused them.
• Experiments can be used to introduce new ideas or to clarify puzzling aspects of topics with which students typically struggle.
• Inductive Method: Induction is the form of reasoning in which a general law or principle is derived from a study of particular objects or specific processes.

Theorem - A mathematical statement whose truth has been established (proved) is called a theorem.For example, 

• The sum of the interior angles of a triangle is 180º.
• The product of two even natural numbers is even.

Key PointsMathematical theorem:

• The theorems in mathematics are dependent on the abstract nature of mathematics.
• Theorems are generally referred to as mathematical statements that can be proved with the use of logical reasoning.
• A theorem can be in the form of an implication i.e., any hint or suggestion as the theorem are general statements of mathematics that are proved using definite methods and logical reasoning.
• The theorem can be proved by using more than one method.
• Firstly the hypothesis needs to be formed, then the statement is being proved with the use of logical reasoning. So, theorems have proof based on logical reasoning and hypothesis.
• A theorem can be bi-conditional as if one condition is true then the other condition of the theorem has to be true. For example, if the sum of two angles of a triangle is 90 degrees then the third angle of a triangle has to be 90 degrees. (The sum of all three angles of a triangle is 180 degrees).

Therefore, it can be said that there is only one way to prove any theorem is not true about a mathematical theorem.

Additional Information

• An axiom is a mathematical statement that is assumed to be true without proof.
• A conjecture is a mathematical statement whose truth or falsity is yet to be established.

The term professional development refers to in-service training to upgrade the knowledge base and skills of the trainees.

• In the context of teachers, professional development facilitates in-service training wherein the teachers get an opportunity to upgrade their content knowledge and pedagogical skills.

Key PointsProfessional development programs for mathematics teachers are designed to be comprehensive and rigorous, equipping the teachers with a wide-ranging set of pedagogical skills to become more effective in their classrooms.

Organizing and participating in such professional development programs help the teachers in the following ways:

• Become more attuned to the latest developments in the field of mathematics.
• Develop greater commitment toward their learners
• Create a platform for sharing professional experience
• Work towards continuous improvement of their teaching skills
• Keep abreast of skills required to adapt to ever-changing learners' curriculum
• Timely inservice training programs to help teachers upgrade their pedagogy.
• Enhancing teachers' knowledge through seminars and conferences.
• Getting teachers involved in various mathematics clubs and inter-university activities.
• Seminars/ Conferences/ Workshops to learn from a variety of expertise from around the state or country.
• Observation teachers observe other teachers improve their skills.

If a teacher involves in activities other than Teaching and education, they will not focus on content and hence this will affect the learning of students.

Therefore, Giving duties to teachers in the implementation of policies does not lead to the professional development of mathematics teachers

Trigonometry is a word derived from three Greek words- ‘Tri-Gon’ meaning ‘Three Sides’ and ‘Metron’ meaning ‘to measure’. Thus Trigonometry means the measurement of the sides and angles of a triangle. It has its application in astronomy, geography, surveying, engineering, navigation, etc.

Key PointsA clinometer is referred to as an instrument used for measuring the angle of slope, elevation, or inclination of an object.

How to use -

• First Hold the clinometer out at arm's length.
• Sight along with it, until the eye and arm make a straight line to the top of the tree.
• Someone else should then read off the angle made by the plumb line on the protractor (Z).
  

Thus, a device that students should use to find heights and distances of distant buildings or poles by applying trigonometric ratios is a clinometer.

Additional Information

• A protractor refers to the instrument that helps measure an angle and the units of measurements obtained using a protractor are degrees.
• A thermometer refers to the instrument that is used for measuring temperature.
• Set-square refers to an instrument for drawing straight lines and angles. It is in the shape of a triangle with one angle of 90º.

In the assessment of learning, we have to use a variety of tools and strategies depending on the nature of the task to be assessed. Examples of some tools used in the assessment of learning are-

• Tests using various types of questions
• Anecdotal records (descriptions of important events in the life of the student related to the task or process being assessed)
• Rating scales
• Checklists etc.

Key PointsData from multiple sources enriches decision-making about learning that leads to increased results for every student.

Multiple sources include

• Formative and summative assessments
• Performance assessments
• Observations
• Work samples
• Portfolios
• Assignments
• Projects and self-reports, etc.

Therefore, we can conclude that Observation, anecdotal records, maintenance of rubrics, assignments, etc. are terms associated with tools and techniques of assessment.

Additional Information

• An observational technique implies the use of a particular observational tool such as a checklist, rating scale, or anecdotal record by observing students in a natural setting (also in a simulated setting) is a useful technique for gathering data about student’s performance in different curricular and co-curricular activities and their effective behavior.
• Projects can help the teacher to get information about the student’s ability in applying the knowledge in different situations. Besides, it enables the teacher to know the student’s skills in recording the data, analysis of the data, and documentation the project.
• A rubric is a scoring tool created by experts, teachers, or both teachers and students for assessment of student’s performance in any area, including curricular subjects, curricular activities, and socio-personal qualities.

The recreational activities which are almost ignored in our schools should be given importance as they motivate the students and develop a positive attitude among the students. 

Key Points

• Mathematics club is the most effective way to enhance student's learning beyond school hours.
• Mathematics club is a group of individuals getting together to organize events, discuss, debate on various topics pertaining to mathematics.
• It initiates and develops mathematical expression among the students.
• Math clubs help learners to engage in various activities related to mathematics learning.
• The mathematics club will be a medium of developing student's interest in the subject.

Thus, we can conclude that Forming mathematics clubs which involves various activities related to mathematics learning for students is considered to be the most effective way to enhance students' interest in mathematics beyond school hours.

Rest three options can be practiced during school hours as well*.*

A Number line refers to a straight line with numbers placed at equal intervals.

• A number line can be extended infinitely in any direction and is usually represented horizontally.
• ​0, 1, -1, 2, -2, 3, -3 … These numbers are called Integers. Numbers 1, 2, 3, 4… are called positive integers and -1, -2, -3, -4… are called negative integers.
• Number Zero (0) is the only integer that is neither positive nor negative.

 

Key PointsUsing a number line showing integers and illustrating forward and backward shifts take care of a multi-sensory approach that is the activities included for hands-on experience may include seeing, listening, assembling, fixing, moving, etc.

• The students in classes should be taught through various activities and hands-on experiences.
• Avoid situations where the students are passive listeners for a long period.
• Provide students with hands-on activities such as experiments, observation projects, etc.
• Encourage participation of students in classroom discussions and other collaborative activities.
• In hands-on experience, the learner gets an opportunity to handle, say, equipment, instruments, and other such materials by him or themselves.
• The questions which only check procedural learning, rote memorization, and drill do not initiate the mathematical thinking of students.

Thus, Using a number line showing integers and illustrating forward and backward shift be the most appropriate way to teach the addition of integers to students in 7th grade.

Fractions are defined as the numerical values that are a part of the whole.

Key Points

• Area model: In this model, the fraction is represented as parts of an area or region. Rectangular or circular fraction sets, pattern blocks, geoboards, and tangrams are useful manipulative.With these visuals, fractions are based on parts of an area. Area is a good place to begin fraction explorations because it lends itself to equal sharing and partitioning.
• Length model: With length models, lengths or measurements are compared instead of areas. Either physical materials are compared on the basis of length or number lines are subdivided.. Length models are very important in developing student understanding of fractions.
• Set model:- In set models, the whole is understood to be a set of objects, and subsets of the whole make up fractional parts. For example, 3 objects are one‐fourth of a set of 12 objects. The set of 12 in this example represents the unit, the whole or 1.

Thus, it is concluded that Division model  may not be an appropriate model for teaching fractions in the middle school.

The National Curriculum Framework (NCF 2005) provides the framework for making syllabus, textbooks, and teaching practices within the school education program in India.

Key PointsWhat mathematics offers is a way of doing things: to be able to solve mathematical problems, and more generally, to have the right attitude toward problem-solving and to be able to attack all kinds of problems in a systematic manner.

This calls for a curriculum that is ambitious, coherent, and teaches important mathematics.

• It should be ambitious in the sense that it seeks to achieve the higher aim mentioned above rather than (only) the narrower aim.
• It should be coherent in the sense that the variety of methods and skills available piecemeal (in arithmetic, algebra, geometry) cohere into an ability to address problems that come from science and social studies in high school.
• It should be important mathematics in the sense that students feel the need to solve such problems, that teachers and students find it worth their time and energy to address these problems, and that mathematicians consider it a mathematically worthwhile activity.

Therefore, According to National Curriculum Framework 2005, the goal of mathematics teaching in the school curriculum is that children learn "Important Mathematics". Important Mathematics implies the mathematics that includes meaningful problems, which teachers and students consider worth solving and as part of their daily lives.

Van Heile's theory provides an insight to the teacher about how the students learn geometry at different levels.

• It helps in describing how the students learn at each level and pass to another level and shapes their learning of geometry at each level of learning.

Key PointsThe Van Hiele levels are described below:

• Level 0: Visualization-The students can recognize shapes by their whole appearance that should just like the exact shape. They can also compare the figures with their prototypes (exemplar) or everyday things but can not identify the properties of geometric figures. For example, they can compare the shape of a circle with bangles, coins, wheels, etc. but are unable to identify and describe the properties of a circle.

They will not be able to recognize the shapes if they are rotated upside down. It belongs mostly to the elementary level classes.

• Level 1: Analysis -They will learn the functions and parts of a figure. They can describe the properties of a figure and recognize the figures with the same properties. For example, they can identify the shapes and describe their properties such as a circle is a closed rounded figure with no corners.

It belongs to the upper level of elementary level classes.

• Level 2: Abstraction or informal deduction -The students will be able to understand the relationships between the properties of a figure. They can take part in informal deductive discussions and can discuss the different characteristics of figures**. For example, the opposite sides of a parallelogram are parallel. The opposite sides of a square and rectangle are also parallel which means the square and rectangle are also a parallelogram.**

It generally belongs to the upper elementary classes.

• Level 3: Deduction or formal deduction -At this level, the students become aware of the more complex geometrical concepts. They can prove an abstract statement on geometric properties to conclude*. For example, they can prove that the square is a rectangle but a rectangle can not be a square.*

It belongs to the higher level of classes where students usually combine a certain set of elements to prove any theorem to draw conclusions or do the evaluation.

• Level 4:Rigor -The last level of geometrical learning belongs to the senior secondary and university-level classes. The students can compare different geometrical results*. For example, the sum of all three angles of a triangle is 180 degrees and is compared to the other properties or other results (to find exterior or interior angles of a triangle) related to the triangle to solve geometrical problems.*

Therefore, According to Van Hieles' levels of development of geometrical thinking level - 2 (Relationships) is represented when a Child can informally deduce general properties of a given geometrical shape and can see the linkages among these properties.

Concept:

• Vitamins are a group of organic compounds which are essential for normal growth and nutrition and are required in very small amounts for maintaining optimum growth and good health.
• Their absence causes specific deficiency diseases.
• There are two kinds of vitamins:
• fat-soluble and water-soluble.
• Vitamin A, D, E, and K are fat-soluble.
• While Vitamin B group and Vitamin C are water-soluble.
• Whenever you eat food sources that contain fat-soluble vitamins, the vitamins are put away in the fat tissues in your body and in your liver.

Explanation:

So from the above explanation, the correct option is (3).

Concept-

A cactus plant can survive in the desert because of the following features-

• It has long roots that dive deep inside the soil for absorbing water.
• Its leaves are modified as spines to prevent water loss due to transpiration.
• Its stem is covered with a thick waxy layer to hold water.
• Large and fleshy stems for water storage.
• Thorns and glossy spiky leaves decrease the loss of water.
• Spikes shield cactus from animals that try to utilize stored water.

Explanation-

(a) Leaves are in the form of spines- The leaves of the cactus plant are modified into the spine since it assists them with losing less water during transpiration and furthermore protects them from being eaten by animals. Hence, this statement is correct.

(b) Stem is succulent and performs the function of the leaf- The modified stem of the cactus is referred to as "succulent" since it contains specific tissues for effective storage of water. The stems are green coloured and perform photosynthesis instead of leaves.  Hence, this given statement is also correct.

(c) Stem is covered with a thick layer of wax- The stem of the cactus is covered with a thick layer to retain the water. Hence this statement is also correct.

 (d) Roots lie near the surface-  The cactus has long deep roots for the better absorption of water, and they don't lie near the surface. Hence this statement is incorrect.

So from the above explanation option (1) is correct.

Concept:

• Group 1, 2, and lanthanides from basic compounds of oxygen when they react with dioxygen.
• When a metal reacts with oxygen, the resultant oxide is a base.
• Whenever red litmus paper comes into contact with any basic substance, it becomes blue.
• A few instances of basic substances are ammonia gas, milk of magnesia, baking soda, and limewater.

Explanation-

• Carbon belongs to Group 14, and sulfur belongs to Group 16, hence they can't form bases.
• Calcium and Magnesium belong to the Group 2 of the periodic table.
• Limewater is a solution of calcium hydroxide.
• Carbon dioxide responds with calcium hydroxide solution to produce a white precipitate of calcium carbonate.
• If carbon dioxide rises through limewater, the limewater turns milky or cloudy white.
• Thus, it is used to test carbon dioxide gas.

So, from the above explanation, the correct answer is an option (1).

Confusion Points

• The results from Mg(OH)₂/MgO systems show that CO₂ only slightly reacts with MgO and Mg(OH)₂ during heat storage and release processes.
• This study indicates that carbonic acid (H₂CO₃) could easily react with CaO/Ca(OH)₂ to form CaCO₃ during heat release processes.

Mistake Points As, per the official answer key option (Magnesium), is correct but according to the question, and solution correct option (Calcium) is correct.

Concept :

• The skeletal system functions as the main framework of the body.
• It is the combination of all the bones and tissues associated with cartilages and joints.
• Joints play an important role in the skeletal system as it allows different types of movement at different locations.
• If the skeleton is without joints, then there would be no movement in the human body.
• The skeletal system is divided into axial and appendicular systems.
• An adult body consists of 206 bones

Axial skeleton :

• It runs along the body's central axis and composed of 80 bones and consists of
• Skullbone, Thoracic cage, and Vertebral column

Appendicular skeleton :

• The appendicular skeleton is composed of 126 bones and consists of :
• Pelvic girdle, Upper limbs, Lower limbs, Pectoral girdle

 

 

                    Fig: Human skeletal system

Explanation :

• A joint is a connection that occurs between the bones in the skeletal system.
• The joints provide the means for movement.
• The joints help us to rotate our shoulders, bend our knees and elbows, and move our neck.

Ball and socket joint :

• This type of joint helps in rotatory movement.
• One bone is hooked into the hollow space of another bone.
• Examples: shoulders

    Pivotal joints :

• This type of joint in sideways and back forth movement.
• One bone has tapped into the other in such a way that full rotation is not possible.
• Example: Pivotal joint in the neck

Hinge joints :

• Hinge joints are like hinges in the door, where only back and forth movement is possible.
• Examples are ankle, elbows, and knee joints.

Fixed joints : 

• In this type of joint bones are fused together in such a way that they are anchored to the component, mostly to form a fixed structure. Examples are the skull and upper jaw.

So, the correct answer is option(1)

Additional InformationGliding joint :

• This joint allows two or more round or flat bones to freely move or slide together without rubbing.
• Examples are the wrist, palm, ankle, and sole

Saddle joint :

• This type of joint does not allow rotation, it does not allow for back and forth movement as well as side to side movement.
• Examples: Thumb

Concept-

Proteins: They are a sort of biomolecules that are comprised of amino acids. A protein is comprised of a few amino acids that are connected together by peptide bonds. They play different roles like helping in the development, repairing cells, and keeping us healthy.

Explanation-

Deficiency due to Proteins:

• A serious lack of protein in children can cause swelling, liver fat, skin degeneration, increment the seriousness of the infection, and stunt development.
• A continuous supply of amino acids is hence essential.
• This is the reason why doctors advised us to include more egg whites, pulses, grams, etc in our diet for the proper growth and development of a child.

Deficiency due to fats-​ 

• When you don't get sufficient fat in your eating routine, you might see side effects like dry rashes, balding, a weak immune system, and issues connected with a lack of vitamins.
• To assist with keeping up with great well-being, a large portion of the fats you eat ought to be monounsaturated or polyunsaturated fats.

Deficiency due to carbohydrates

• Our body can store additional carbohydrates in your muscles and liver for use when you're not getting an adequate number of starches in your diet.
• A carb insufficient diet might cause headaches, weakness, nausea, constipation, bad breath, and nutrient and mineral deficiencies.

Deficiency due to minerals 

• The most common example of this deficiency is iron deficiency, zinc deficiency, and magnesium deficiency.

Its symptoms include loss of appetite, muscle cramping, abdominal pain, constipation, and diarrhoea.

 

So from the above explanation, the correct option is (2).

Concept-

Asexual Reproduction:

• A type of reproduction where offspring is delivered by a single parent without the fusion of gametes.
• A single parent produces offspring and the offsprings are precise duplicates of their parents.
• The offsprings are hereditarily and morphologically identical and referred to as clones.
• The various sorts of asexual reproduction are binary fission, budding, vegetative propagation, spore formation (sporogenesis), fragmentation, parthenogenesis, and apomixis.
• The organisms that replicate through asexual means are bacteria, archaea, many plants, fungi, and certain animals.

Explanation:

1) Mode of asexual reproduction in algae- Small green algae reproduce by fragmentation while large algae reproduce by spore formation.

2) Mode of asexual reproduction in fungi- Budding, fission, and fragmentation are the main modes of replication in fungi, the majority reproduce asexually from spore formation.

3) Mode of asexual reproduction in dahlia- Vegetative propagation is the method of asexual reproduction, it is developed by fasciculated tuberous roots in dahlia. 

4) Mode of asexual reproduction in cactus- Vegetative cloning or vegetative propagation is the asexual mode in cactus and it occurs when a mature plant detaches itself and develops into a new plant.

So, from the above explanation, the correct answer is an option (4).

Concept : 

Substances :

• A substance is a pure form of matter that contains only one type of atom or molecule.
• On the other hand, a mixture contains a combination of different atoms or molecules and thus it is impure.

Types of substances : 

• Elements: These are the simplest form of matter which cannot be broken down into smaller components. Examples are carbon (C), Hydrogen (H), Oxygen (O), Sodium (Na), and many more.
• Compounds: These are made up of two or more different elements bound together by chemical bonds. Examples are carbon dioxide (CO2), sodium hydroxide (NaOH), table salt( NaCl), and many more.

               

                                                                                                                                         Explanation :

Storage of Sodium : 

• Sodium is a member of the alkali metal family being in group 1 of the periodic table.
• Sodium is a very reactive metal and it is kept in kerosene to prevent it from coming in contact with oxygen and moisture. If it happens, it will react with the moisture present in the air to form sodium hydroxide, and this is an exothermic reaction that generates lots of heat.

Na + H₂O → NaOH + H₂

Storage of Phosphorus :

• Phosphorus is an element of group 15 in period 3.
• Phosphorus is a highly reactive element.
• There are four types of phosphorus :

1. Red phosphorus  2) White phosphorus 3) Yellow phosphorus  4) Black phosphorus

• Phosphorus is stored underwater preventing it from catching fire spontaneously due to its highly reactive nature.

Storage of Sodium hydroxide :

• Sodium hydroxide is a powerful and extremely corrosive alkali that decomposes living tissues.
• Its solution is highly exothermic which can cause burns when comes in contact with skin.
• When it comes in contact with the eyes can lead to eye blindness.
• Sodium hydroxide is stored In an airtight plastic container, the use of a glass container should be avoided.

Storage of Mercury : 

• Mercury( Hg) is an element located in period 6 and group 12 and it is liquid at ordinary temperature.
• It is also known as quicksilver or silvery-white liquid.
• Mercury is a liquid that can flow but does not stick to the glass and hence can be stored in glass.
• It has a high coefficient of expansion and surface tension.

So, the correct answer is option (2)

Additional Information

• Sodium (Na) is used as fertilizer when it bonds with chlorine (Cl) to form sodium chloride (NaCl).
• Phosphorus  is used in baking powder, fertilizers, and fireworks
• Phosphorus helps in the formation of bones and teeth.
• Mercury vapors are used in streetlights and advertising signs.

Concept :

• The human body needs glucose (carbohydrates) for producing energy for all the processes undergoing in the body.
• During anaerobic respiration, when sufficient oxygen is not available for the body to convert glucose into energy**, leads to fatigue** in the body.
• The food we eat breaks down and changes into a monosaccharide unit of carbohydrate i.e. Glucose.
• The glucose which is derived from food gives energy to our body.
• This happens when oxygen reacts with glucose and converts it into energy.

Explanation :

• When we perform the rigorous exercise, our body needs oxygen to meet the energy requirement.
• But, sometimes our body may not be able to provide sufficient oxygen in the body while doing intense exercise.
• As the level of oxygen decreases in our blood, the glucose breaks down through anaerobic respiration.
• Due to a lack of oxygen, the glucose forms lactate, and hydrogen ions combine to form lactic acid.
• The lactic acid in turn gets converted to energy, but the rate of accumulation is faster, and hence lactic acid gets accumulated in the muscles.
• This causes cramps in the muscles.
• Hence, during exercise glucose is converted to lactic acid due to a lack of oxygen.

So,  the correct answer is option is 3

Key Points 

• The lactic acid( C₃H₆O₃)  produced in our body after intense exercise is harmless and does not cause any damage to the body.
• After the level of lactic acid decreases in our muscles, we reach our original condition.

Additional Information

Concept :

Manure :

• Manure is the decomposed form of dead plants and animals which is added to the soil to improve soil quality and production.
• It is a natural form of fertilizer
• It is cost-effective.
• It is highly rich in organic matter and humus and thus increases soil fertility.

Sources of manure :

• Wastes from human habitation such as domestic waste, sludge, and human urine.
• Animal waste like cattle dung, wastes from slaughterhouses, and slurry from biogas plants.
• By-products of agricultural industries.
• Crop waste like weeds.

Types of manure : 

• Compost manure: It improves the soil structure and water holding capacity of the soil and thereby improves the health of the soil.
• Green manure: It increases the nutrient content in the soil and helps in the prevention of soil erosion and the growth of weeds.
• Farmyard manure: It improves the soil structure and is used as a natural fertilizer. It increases the water-holding capacity of the soil.

    

               Fig: Mineralisation of soil

Explanation :

Functions of manure :

• Increases soil fertility by enriching the soil with decomposed organic matter.
• Reduces soil erosion and leaching by amending the soil.
• Improves the water and nutrient holding capacity of the soil.
• It contains a large number of fibers, undigested animal feed, and sawdust which increases the nutrient content of the soil.
• Methane gas which evolved as the by-product of manure can be used for cooking purposes.

So, the correct answer is option (3).

Additional Information

• Vermicomposting: It is a method to recycle agricultural wastes and prepare compost with the help of earthworms. Earthworms consume biomass and excrete it in the form of worm casts. Worm casts are also known as black gold because they enrich the soil many more times than other compost.
• Difference between charcoal and biochar

 

• Difference between manure and fertilizer

Concept : 

• Virus:  A virus is a microscopic infection-causing agent that replicates only inside the living cells of an organism( Host).Bacteria: A bacteria is a biological cell, which consists of a large group of microscopic organisms.
• The disease is a state of experience by the body when one or more systems of the body are not functioning normally.
• Diseases are caused by bacteria, viruses, or pathogens.
• The common cold is the most common type of viral infection that is caused by infections in the respiratory tract.
• Some viral diseases are Chickenpox, Influenza, AIDS, Mumps, Measles, Viral Hepatitis, Covid-19, and many more.

Causes of viral diseases :

• Viral diseases are mainly **caused when a virus enters the human body(Host )**and uses its host machinery to reproduce.
• If the host's immune system fails to fight against viruses, it multiplies and spreads to other cells in the body causing more infections.

Symptoms of viral diseases :

• Sneezing
• Fever with fatigue, sore throat, headache
• Irritability
• Swollen tonsils
• Rashes
• Excessive weight loss

Explanation : 

So, the correct answer is an option (2).

Additional Information Measles-Rubella (MR) Vaccination Campaign

• This campaign was launched by The Union Ministry of Health and Family Welfare.
• It intends to cover more than 40 crore children
• MMR vaccine is given to children against three diseases measles, mumps, rubella
• Five countries have eliminated measles. Bhutan, DPR Korea, Maldives, Sri Lanka, and Timor Leste
• The liver is infected in the disease Hepatitis A.
• Covid -19 is a disease caused by a virus called Sars-Cov-2.

Explanation:

Uses of coke :

• It is used as a fuel for stoves and furnaces and also used by blacksmiths.
• It is used to produce iron in a blast furnace.
• It is used to manufacture steel and other materials.
• The amount of carbon content in coke is so high that is said to be an almost purest form of carbon.

Uses of coal tar :

• It is used in manufacturing paints, perfumes, synthetic drugs, dyes, etc.
• It is also used in the making of insecticides, pesticides, etc.
• It is widely used in making shampoos, soaps, and ointments.
• Photographic materials are made up of coal tar.
• Coal tar is an active ingredient in lice repelling shampoos.

Uses of coal gas :

• It is used in municipal lighting.
• it is used as fuel.
• it is used for heating.
• It is used as an illuminant.
• It is highly toxic because nitrogen in coal reacts with oxygen in the air to form nitrogen oxides.

N₂ (g) + O₂ (g) → 2NO (g)

• Nitrogen oxides can react with them to produce ozone and other contaminants.

​Uses of bitumen :

• It is used for construction purposes mainly metalling of the roads.
• It is used in roofing and used for waterproofing.
• Mainly it is used for road construction due to its durability.
• The primary use (70%) of bitumen is in road construction, where it is used as a binder mixed with aggregate particles to create asphalt concrete which makes the surface of roads more smooth.

So, from the above, it's clear that option 1 is correct one.

Additional Information 

 Difference between coal gas and natural gas:

Concept : 

• Fibres are defined as thread-like structures that are thin, long and flexible strands.
• The two main sources of fibre are Plants and Animals.
• Plant fibres are obtained from plant sources like cotton, jute, bamboo, coconut trees, flax seeds, vegetable fibres, wood, grains etc.

Explanation : 

Cotton :

• Cotton is a soft fibre that is obtained from cotton plants and grows as a ball.
• Cotton is basically grown in Maharashtra, Rajasthan, Madhya Pradesh, Gujrat etc.
• When cotton plants start flowering, yellowish-white flowers grow and after a few days, they turn red in colour.
• Later on, flowers change into cotton balls.

Flax :

• Flax also known as linseed with the binominal name Linum usitatissimum, is a member of the genus Linum in the family Linaceace.
• It is a food and fibre crop grown in cooler regions of India.
• Flax fibre is extracted from the skin of the stem of the plant.
• Flax fibre is a soft, lustrous and flexible, bundle of fibre that looks like blonde hair.
• It is stronger than cotton fibres but less elastic.

Silk :

• Silk is a natural protein fibre, some forms of which can be woven into textiles.
• The protein fibre of silk is composed mainly of fibroin and is produced by silkworm larvae to form cocoons.
• The caterpillar/ silkworm secretes fibre made up of a protein which gets hardened on being exposed to air and becomes silk fibres
• Silkworm completely covers themselves with silk fibres and this covering is called a cocoon, which is further processed to obtain silk fibres.

Coconut fibre :

• Coconut fibre (coir) is a natural fibre obtained from the husk or the mesocarp of coconut ) cocus Nucifera).
• The fibre is typically golden in colour after cleaning up, it is also known as golden fibre.
• It is fibrous and tough.
• Its individual fibre cells are hollow and narrow having thick walls containing cellulose.
• Coconut fibres are used for making mattresses., brushes, floor mats etc.

So, the correct answer is option (2).

Important Points

 

Additional Information

• Jute: These plants require standing water and alluvial soil to grow well.
• Angora wool: The fur of the rabbit hair is extremely soft to touch, thus due to its desirable characteristics, they are in high demand and quite expensive.

Concept :

Polymer:

• Polymers are materials made of long, repeating chains of molecules.
• The materials have unique properties depending on the type of molecules being bonded.
• Some polymers bend and stretch, like rubber and polyester.
• Others are hard and tough like glass and epoxies
• Plastics are polymers and man-made substances.
• Plastics generally have the following properties :
• They are resistant to corrosion and chemicals
• They have high strength to weight ratio.
• They are resistant to shock and are water-resistant
• Have good durability and are cost-effective
• They are light in weight and non-reactive to chemicals and solutions.

Explanation :

Thermoplastics :

• They are polymers that can be deformed on heating and be reformed into different shapes.
• Examples:  Polythene, Polypropylene, Polystyrene, Polyvinyl chloride (PVC)

Thermosetting  plastics :

• They are polymers that cannot be deformed on heating or remolded into a new shape.
• Thermosetting plastics are polymers that become irreversibly rigid on heating.
• Initially, it is in a liquid state when heated it forms a covalent bond by crosslinking the polymer units and it becomes rigid.
• Examples: Bakelite, epoxy resin, melamine, etc.
• So, the correct answer is an option (1).

 

Additional Information

• Ethylene is used in plastics.
• It is the simplest alkene.
• Polyethylene is used in agriculture for the ripening of fruits.
• Thermosetting plastics are used in making kitchenware, floor tile, and electrical switches. etc.

Mistake Points As, per the official answer key option 3 is correct but, according to the question statement option, 1 is the correct one.

Calculation :

Given:

Speed of  rabbit = 56 Km/hr

Distance covered = 2.5 Km

Time=?

We know that Speed= Distance/ Time

 56 = 2.5/ Time

Therefore Time = 2.5/ 56 

 = 0.044 hr

Changing hours into minutes = 0.44 × 60

 = approximately 2.64 minutes

 = 3 minutes

So, the correct answer is option is (1) i.e. 3 minutes

Concept :

• Clinical thermometers are meant for clinical purposes.
• It is developed for measuring the human body temperature.
• It is a long narrow glass tube with a bulb containing mercury at the end.
• The normal body temperature is 37° C, which fluctuates between 35º C to 42º C.
• Hence the level of mercury tells our body temperature in ºC.
• Since mercury is a toxic element, thus these thermometers are being replaced by digital thermometers.

​Explanation :

Reading of thermometer :

• Firstly clean and sterilize the thermometer.
• Jerk the thermometer so that the mercury is brought to the glass bulb.
• Note the temperature difference between two bigger marks on the scale of the thermometer.
• For example, the difference is 1 degree.
• If there are 5 divisions between the two consecutive bigger marks, then one smaller division will be equal to 0.2º C
• So, according to the question, where it is two-division more to the right side, the temperature is 101.4 degrees.

Precautions : 

• The thermometer is to be placed under the tongue inside the mouth of the patient to get the temperature of the body.
• When the reading is taken, the thermometer needs to be held vertically to eye level with the top of the mercury in the capillary thread.
• So, the correct answer is option (1).

Additional Information

• ​ The medical thermometer began as an instrument more appropriately called a water thermoscope, constructed by Gallileo Galilei circa 1592-1593.

Concept :

Thunderstorm

• A thunderstorm is a loud noise that follows a flash of lightning.
• During a thunderstorm, the air currents move upward while the water droplets move downward.
• Separation of charges occurs due to this and causes the accumulation of positive charges at the upper part and negatively charged at the lower end.
• The difference in charge causes the flow of current which is called lightning.
• This may cause damage to life and property.
• To be safe from such a situation, we should avoid using conductors.

Explanation :

• In the situation of a thunderstorm, one must stand away from electrical equipment and wiring, corded phones must not be used during a thunderstorm.

Precautions to be taken during thunderstorms:

• Don't take shelter under a tall tree as lightning strikes the tall objects.
• Use a mobile phone instead of a corded phone because transmission of current in wires may lead to shock.
• Take shelter inside a car. Lightning will travel along the metallic surface of the car to the ground.
• The shelter can be taken in buildings. Lightning will travel to the ground due to earthing of buildings.
• Squatting low on the ground can lessen the chance of attracting a direct hit from a strike.
• Thus, the correct answer is an option (1)

Additional Information Lightning conductors ;

• A lightning conductor is a device used to protect buildings from the damaging effect of lightning.
• Lightning consists of a metallic rod, taller than the building, which is installed on the walls of the building during its construction.
• One of the rods is kept out in the air and the other lowered is buried deep in the ground.
• Hence lightning hits the ground, it
• 

                 Fig. Lightning protection system

Mistake Points As, per the official answer key option 3 is correct, but according to the question pattern option, 1 is the correct one.

The correct answer is Vacuum.

Key Points

• Sound is a mechanical wave, which means it requires a material medium such as solid, liquid, or gas to travel.
• It is the movement of the medium that transmits the wave.
• The sound waves travel through these mediums by vibrations of the molecules in the matter(solid, liquid, gas)
• Sound needs a medium to travel.

Explanation :

• The molecules in solids are packed very tightly
• The molecules in the liquid are not tightly packed as in solids
• The molecules are very loosely packed.
• The spacing between the molecules enables sound to travel faster through a solid than a liquid and a gas.

 Solids> Liquids> Gases                                         

• Sound travels about four times faster in water(liquid) than it does in the air(gas)
• So sound waves are vibrations of particles that travel in air, water, and solid.

So sound cannot travel through empty space(vacuum) where there is no medium.

So the correct option is (4) Vacuum.

Additional Information

• Frequency of sound: The number of rarefactions and compressions that occur per unit time is known as the frequency of a sound wave.

    $f=1/T$

 where f is the frequency of the sound wave and T is the time period.

• Speed of sound: The formula used to calculate the speed of sound is given as :

  $c=d/t$ 

where d is the distance traveled by sound and t is the time taken to cover the distance

Concept :

Pressure 

• It is the amount of force that is exerted on the surface.
• Gravity causes pressure naturally.
• Water pressure is the force created by the weight of water.
• Water pressure can push water through pipes and hoses.

The formula for water pressure is :

Water pressure= p g h

• p = density of water in kg.m-3
• g = gravitational force in 9.81 m.s-2
• h = height in m
• SI unit of pressure is Pascal (Pa)

Explanation :

• In the four glass cylinders A, B, C, D  we observe that :

1. The stream coming out from cylinder D i.e**.12 cm** hole land nearest to the cylinder.
2. The stream coming out from cylinder A i.e**. 5** cm hole land farthest to the cylinder.

This phenomenon is created by different water pressure at each hole.

• Water pressure is the force applied from the water above to the water below.
• Because this force comes from the weight of the water, the water at the bottom receives the most water pressure.
• High water pressure pushes the water out through the hole the strongest and therefore the stream shoots the farthest.

 

                 

 Fig:  Water pressure increases with depth

Therefore the correct answer is option is (1).

Explanation :

Pinhole camera :

• The pinhole camera is a simple camera that does not have a lens.
• It has a small hole and a lightproof box with a small hole on one side.
• The light from the object goes through the aperture and it projects the inverted image on the opposite side of the box.

Principle of working :

• The image that is formed displays rectilinear light propagation which means the pinhole camera works on the theory that light moves in a straight line.
• When the shutter is opened, the light illuminates thus forming the image on the film which is placed on the backside of the paper.

Use :

• It can be used for surveillance since they are difficult to detect.

Kaleidoscope

• A kaleidoscope is an optical instrument that contains two or more reflecting surfaces tilted towards each other at a certain angle for obtaining a symmetrical pattern when viewed from the other end.
• The tube consists of reflecting surfaces that contain colored pieces of glass.
• If we rotate the tube, we can see symmetrical images are formed.

Principle of working :

• The laws of reflection and the white light is a combination of VIBGYOR that form the basis of the principle of a kaleidoscope.
• When the light falls on the surface of a mirror, it gets reflected in a way that the angle of incidence is equal to the angle of reflection.
• When the white light (VIBGYOR) passes through the colored objects in a kaleidoscope, most of the light gets absorbed by these objects.
• As a result of the multiple reflections of light, there is a creation of beautiful patterns.

Use:

• Fashion designers use the beautiful patterns created by a kaleidoscope.

Periscope :

• A periscope is an instrument for observation around an object in presence of an obstacle or condition. that prevents generally the direct line of sight observation from an observer's position.
• Periscopes permit view outside of the vehicle without cutting the weaker vision openings in the front and side armor protecting the vehicles.

Principle :

• A periscope works on the laws of reflection which states that the light from the objects falls on one mirror at a 450 angle from the object and is reflected.
• This reflected light then falls on another mirror and is again reflected until it reaches the human eye.
• The reflection of light then bounces off an object.

Use :

• Periscope allows a submarine when submerged at a relatively shallow depth to search visually for nearby targets in or out of the water.

Newton's disk :

• Newton's disc is a disc with segments in rainbow colors.
• When the disc is rotated, the color fade to white.
• In this way, Issac Newton demonstrated that white light is a combination of the seven different colors found in a rainbow.

Working :

• Newton made the color disc to prove that white light is a combination of seven colors.
• So, he took a circular disc and painted seven different colors (VIBGYOR ).
• He rotated at high speed then the disc appeared to be white.

 So, the correct answer is option is (2).

Concept :

• The nucleus is a spherical, double-membrane cell organelle that contains genetic material. It is found only in Eukaryotic cells.
• It is also known as the brain of the cell and serves as the control center of the cell.
• It is enclosed in a membrane known as the nuclear membrane.
• A nuclear membrane has small holes called nuclear pores which allow content to move in and out of the cell.

 Eukaryotic cells: 

• These are the cells that contain a membrane-bound nucleus and organelles.

 Explanation:

Functions of the nucleus:

• It contains genetic material and controls cell growth and reproduction.
• It helps in producing copies of DNA and this process is called DNA replication.
• It helps in creating copies of the genome which may be moved out of the cell and read by the rest of the cell. This is called Transcription.
• It also helps in coordinating important cellular activities such as cell division, growth, protein synthesis, and other important functions.

So, the correct option is (a) to provide shape and rigidity to the cell.

Additional Information

Nucleolus-

• The nucleolus is the distinct structure present in the nucleus of eukaryotic cells.
• The nucleolus is composed of RNA and proteins
• It participates in assembling the ribosomes, and alteration of transfer RNA.

Mitochondria-

• Mitochondria are cell organelles or parts of a eukaryote cell. They are in the cytoplasm, not the nucleus.
• They make most of the cell's supply of adenosine triphosphate (ATP), a molecule that cells use as a source of energy.

Ribosomes-

• The ribosome is a complex molecule made of ribosomal RNA molecules and proteins.
• It forms a factory for protein synthesis in cells.

Important PointsDifference between nucleus and nucleolus

The goal of divergent thinking is to generate many different ideas about a topic in a short period.

• It involves breaking a topic down into its various parts to gain insight into the various aspects of the topic.
• Divergent thinking typically occurs in a spontaneous, free-flowing manner, such that the ideas are generated in a random, unorganized fashion.

Key Points

• Divergent thinking questions: These questions ask for more than one response. Children will give a variety of responses and they are all relevant. In the examination system of today, we insist on a single answer, which to teacher dictated only.
• Creative thinking aims at novelty in the first instance rather than truth. Because it aims at novelty, it necessarily has to be different from the conventional modes of thinking. Hence, creative thinking is labeled in psychology as divergent thinking. The outcome of creative thinking, however, has to be validated only by critical thinking.

METHODS THAT STIMULATE DIVERGENT THINKING

• Brainstorming, subject writing, Mind Mapping

Important Points When a teacher asks-

• Write five advantages of solar energy over fossil fuels.
• Draw the labeled diagram of fractional distillation of petroleum.
• List the steps involved in the formation of coal.

These questions have a fixed and precise order of answers. So there is no brainstorming takes place.

• In case of ques - What would happen if all the petroleum reserves are finished up?

Different students give multiple and different answers so the use of critical thinking takes place. 

Therefore, What would happen if all the petroleum reserves are finished up? is an example of a question to assess divergent thinking in learners on the topic of Fossil fuels

A scientific theory is referred to as a structured explanation to explain a group phenomenon in the natural world that often incorporates a scientific hypothesis and scientific laws.

• Science evolves gradually building upon existing knowledge. Scientific theories vary in the extent to which they have been experimentally tested and for how long and in their acceptance in the scientific community.

Key points Scientific theories can be traceable to the acceptance of four matters of fact:

• That something exists;
• That something can be known;
• That there is something which matters;
• That something makes sense and can be reflected upon.

Important PointsAll scientific theories are -

• Closely tied to empirical findings.
• Hence always remains subject to falsification in the event of a contradictory finding. In that sense, scientific knowledge is always provisional.
• They explain the observations based on the given information.
• They can make predictions about the results of future observations.
• Once proven, a theory can be disapproved

Thus, scientific theories explain the observations based on given information and can make predictions about the results of future observations that are correct regarding scientific theories.

In simple words, Science process skills are the processes that are being used by various scientists while doing science. Some common science process skills are Observing, Classifying, Communicating, Measuring, Predicting, and Inferring.

Key Points

• When students visit a garden or local nursery and identify the plants which are 'healthy' and give reasons for identifying those plants as 'healthy' they observe the plants and define them as healthy or unhealthy plants.
• They observe the plants and analyze them and explain the concept practically.

Thus, it is concluded that when a teacher gives the task to the students of class VI Visit a garden or local nursery and identify the plants which are 'healthy' and give reasons for identifying those plants as 'healthy, observing, defining operationally skills are being promoted in this activity.

 

Additional Information

• ​Observing means using our various senses to obtain information (or data) about objects or events attended”. Observations are not to be limited to seeing things only. We use more than one sense organ to collect data (or information) about the objects in our daily acts.
• Defining refers to the thing or idea that something represents.
• Communication in science is a specialized skill through which scientific knowledge is being shared and communicated among the scientific community
• Inferring is using logic to conclude what we observe and an ‘inference’ is an explanation of our observation about any object or event.
• Measuring is concerned with the quantification of our observations. Initially, the school learners learn to measure five basic entities while learning science- length, volume, mass (or weight), temperature, and time.

The expository activity in teaching science is defined as an organized teaching method where information is presented in a specific order.

• This kind of method helps to keep your focus and attention and lays out all of the information you need to know in a way that helps you to remember it.

Key Points

• When a teacher asks open-ended questions and seeks explanations then there is more scope for brainstorming and reflective thinking.
• Encouragement for divergent thinking. More scope for problem-posing and problem-solving.
• Therefore this is not an expository activity because children are not passive recipients of the information.

Therefore, A teacher asking open-ended questions and seeking explanations is not an expository activity in teaching science

Additional Information In the rest three options teacher is just presenting information in an organized manner hence it becomes expository activity.

Gender equity is the process of being fair to women and men. To ensure fairness, strategies and measures must often be available to compensate for women's historical and social disadvantages that prevent women and men from otherwise operating on a level playing field.

Key PointsEquity leads to equality. Gender equality requires equal enjoyment by women and men of socially-valued goods, opportunities, resources, and rewards.

• Where gender inequality exists, it is generally women who are excluded or disadvantaged in relation to decision-making and access to economic and social resources.
• Therefore, a critical aspect of promoting gender equality is the empowerment of women, with a focus on identifying and redressing power imbalances and giving women more autonomy to manage their own lives.

Therefore, Gender equity in science implicates for both girls and boys is correct .

Children while coming to the school already come with many concepts registered in their mind through experience or through knowledge constructed by their elders are community members. They do not come with brains as blank slate something or other is filled in that it may be a correct concept or a misconception. 

Key Points

• S1 is true because children's ideas about a science content or often domain-specific and may be conflicting as every student is different and belongs to a different community so the ideas about science can be domain-specific according to their environment and community and also as each student has a different domain they may develop different concepts which may be conflicting and this issue should be addressed by the teacher peacefully.
• S2 children's alternate conceptions in science demonstrate liner reasoning from cause to effect is also true because children may have some alternate concepts which the main conflict with the real scientific concepts so as the children may have experienced many experiences in their life before coming to school, as a result, this alternate conceptions may be developed in the student cause and effect. As when a certain thing happens the students could believe that this happened due to a particular cause this is known as cause and effect due to which they develop alternate conceptions.

Hence Both S1 and S2 are correct.

Observation and inference both are totally different.

• Observation is considered to be acquiring information through any of the sensors by experimenting and exploring various factors related to the concept. Observation can be clearly seen or heard or felt by the observer and it can be recorded also.
• The inference is like a conclusion that is based on the observation but it can't be directly seen are experienced through any of the senses. The inference is drawn when the expected or positive result is obtained from the observation and it is considered as a generalization.

Key Points

• S1 is an observation as the student can see that when turmeric is added to both solutions solution 1 turned red and there is no change in solution 2.
• S2 is an inference because here the student did not directly observe that Solution A is base and solution B is an acid. But this was an inference developed according to the observations made in S1.

Hence S1 is observation; S2 is an inference.

Open-ended questions are the ones that don't have a fixed solution or a fixed method to arrive at the solution. Here the question has multiple answers and enhances the thinking capacity of students. 

Key PointsAdvantages of open-ended questions:

• These enhance creativity and divergent thinking in children.
• The student has the full scope and freedom to express his views and solved his method.
• Rote memorization is avoided and meaningful, authentic learning takes place.
• The student explores the concept through multiple ways and methods to arrive at the solution which leads to the construction of true knowledge.
• Special skills and talents of children can be identified through open-ended questions.

What would happen if the period of rotation and the revolution of the moon are different is an example of an open-ended question because for this there is no fixed answer in the textbook and the student has to think and understand the concept to answer this question.

Hence the question in option four is an example of an open-ended question. 

Additional Information

• On the other hand, all the other questions are not open-ended as they have a fixed and single answer which can be found by the student in the textbook itself. And these question doesn't need thinking and exploration of the concept.

Assessment for learning also known as formative assessment is designed to identify the learning difficulties and misconceptions of children and accordingly adapt the teaching strategies and provide children with remedial teaching. This assessment happens regularly using many tools. 

Key PointsInvestigatory projects are examples of assessment for learning as:

• Here the students get a chance to collect, understand and analyze the information required for the project.
• Active involvement of students will be there throughout the project as they will be busy doing some of the other activities required for the project completion.
• Here the students will be assessed through observation even when they are doing the project.
• The steps followed by students to complete the investigatory project can be taken as sources of information to understand the cognitive abilities of children and remediate them.
• Here there is a lot of scope for the students to understand their errors, and correct and verify them to as not to repeat them in the further process.

Hence investigatory project is an example of assessment for learning.

Additional Information

Socio-scientific issues are controversial, socially relevant, real-world problems that are informed by science and often include an ethical component. Examples include fish farming, genetic testing, global warming, and captive breeding in zoos. 

Key Points

• Assertion A: Science teachers should discuss socio-scientific topics in the class is true because as per NCF one of the main objectives of teaching science is to make the students identify and understand the issues related to science and try to solve them as the issues occur in the daily life. Discussing socio-scientific topics in the class also makes students good citizens and think of various methods to solve these issues.
• Reason R1 is true and is the correct explanation of A because socio-scientific topics promote multiple perspectives and argumentation skills in learners which are very important for the students in their future and also in the further greats they are going to be promoted in future. This match the students understand the social sciences topics very clearly and act on them when they get a chance shortly. 

Additional Information

• Reason R2 is not a correct explanation because this indicates social scientific topics as controversial and involve multiple perspectives which may make students confused are mislead them which is not true regarding the learning objectives.

Hence A is correct and R1 is correct to explain A.

The correct answer is Both (a) and (b) are wrong

Key Points

• Let's refer to the following line of the passage:
• "There was a woman who was beautiful, who started with all the advantages, yet she had no luck. She married for love, and love turned to dust. She had bonny children, yet she felt they had been thrust upon her, and she could not love them."
  

Thus, it can be inferred that the correct answer is option 4)*.*​

Additional Information

• Comprehension questions can be answered easily by:
• Reading the passage carefully.
• Identifying the purpose of the passage.
• Going through the questions correctly with correct implied meaning.

The correct answer is The lady always suspected that there was something wrong with her.

Key Points

• Let's refer to the second line of the first paragraph:
• "And hurriedly she felt she must cover up some fault in herself. Yet what it was that she must cover up she never knew."
• It can be easily understood from the line that the lady always felt that there was something wrong with her and wanted to cover it up, but was unable to do so, as she never knew what to cover up.
  

Thus, it can be concluded that the correct answer is option 1*.*​

Additional Information

• Comprehension questions can be answered easily by:
• Reading the passage carefully.
• Identifying the purpose of the passage.
• Going through the questions correctly with correct implied meaning.

The correct answer is (c) is right and (a) is wrong.

Key Points 

• Let's refer to the following lines of the passage:
• "Everybody else said of her: 'She is such a good mother. She adores her children'. Only she herself, and her children themselves, knew it was not so. They read it in each other's eyes."
• "She had bonny children, yet she felt they had been thrust upon her, and she could not love them. They looked at her coldly, as if they were finding fault with her."
  

Thus, from above it can be concluded that the correct answer is option 3)*.*​

Additional Information 

• Comprehension questions can be answered easily by:
• Reading the passage carefully.
• Identifying the purpose of the passage.
• Going through the questions correctly with correct implied meaning.

The correct answer is she had inherited a large fortune.

Key Points

• The first line of first paragraph states, "There was a woman who was beautiful, who started with all the advantages, yet she had no luck. She married for love, and love turned to dust. She had bonny children, yet she felt they had been thrust upon her, and she could not love them."
• From the line it can be easily understood that the woman had large fortune (a pleasant house, with a garden, and discreet servants) inherited.
  

*Therefore, it can be concluded that the correct answer is option 4).*​

Additional Information

• Comprehension questions can be answered easily by:
• Reading the passage carefully.
• Identifying the purpose of the passage.
• Going through the questions correctly with correct implied meaning.

The correct answer is they lived in style in spite of everything.

Key Points 

• The last line of the second paragraph states, "There was always the grinding sense of the shortage of money, though the style was always kept up"
• From the line, it can be easily understood that the standard and style of their living were kept up even with the shortage of money.

*Hence, it can be concluded that the correct answer is **option 3.***​

Additional Information

• Comprehension questions can be answered easily by:
• Reading the passage carefully.
• Identifying the purpose of the passage.
• Going through the questions correctly with correct implied meaning.

The correct answer is critical

Key Points 

• Bonny generally means 'attractive or beautiful ( रूपवान, सुन्दर , चंचल ), it is also used to address one's beloved or baby ( किसी के प्यार या बच्चों के लिए प्रयोग होने वाला शब्द )'
• Ex: A bonny child dressed in traditional clothing went to the function.
• Marked option 'Critical' means 'expressing what is wrong about something, describing pros and cons of something ( दोषदर्शी, आलोचनात्‍मक )'
• Ex: The report was very critical of safety guidelines for Covid patients.
• It's clear that 'Bonny' and 'Critical' are different in meaning.
  

Therefore the correct answer is option 2).

Additional Information 

• Let's look at the meaning of other options:
• Attractive: that pleases you or attracts you ( दिलचस्‍प, मोहक, रुचिकर ); nice and beautiful (for a person) ( आकर्षक, मोहक (व्‍यक्ति) )
• Charming: very pleasing or attractive ( बहुत सुखकर, रोचक या आकर्षक )
• Beautiful: very pretty or attractive; one that gives pleasure to the senses ( सुंदर, ख़ूबसूरत, आकर्षक; रमणीय, प्रियकर )

The correct answer is hates.

Key Points 

• Adores generally means 'to love and admire something/somebody very much ( स्‍नेह और आदर की भावना से देखना ); to like something very much ( किसी चीज़ को बहुत पसंद करना )'
• Ex: Kritima adores her elder brother.
• Marked option 'hates' means 'to have a very strong feeling of not liking somebody/something at all ( व्‍यक्ति या वस्‍तु के प्रति अत्‍यधिक अरुचि होना; घृणा करना )'
• Ex: Prakhar hates playing football.
• It's clear that 'Adore' and 'Hate' are opposite in meaning.
  

Therefore the correct answer is option 4).

Additional Information 

• Let us look at the meaning of other options:
• Cherish: to love somebody/something and look after him/her/it carefully ( किसी से स्‍नेह करना और सावधानीपूर्वक देखरेख में रखना )
• Admire: to respect or like somebody/something very much ( किसी के प्रति आदर व प्रशंसा का भाव रखना ); to look at somebody/something with pleasure ( किसी को प्रिय दृष्टि से देखना )
• Adorn: to add something in order to make a thing or person more attractive or beautiful ( अधिक आकर्षक या मोहक बनाने के लिए सजाना )

The correct answer is a Principal

Key Points 

• A clause is a part of a sentence that contains a subject and predicate of its own.
• A Principal clause can exist independently without a subordinate clause.
• ​Ex: I saw the boy who snatched the bracelet.
• 'I saw the boy' itself is complete and can exist independently in the sentence.
• In the above sentence 'Although they lived in style...' is a Principal clause as it can exist without the remaining part of the sentence.
  

Therefore, the correct answer is option 1).

Additional Information 

• A subordinate clause depends on the principal clause and cannot exist without it.
• Hence, its also known as the dependent clause.
• Ex: I played out until it started raining.
• 'Until it started raining' is the subordinate clause.

The correct answer is a Determiner

Key Points 

• 'Such' is a determiner, meaning 'very' or 'to this degree'.
• Use of 'such': such + noun phrase.
• Such is used before a noun, even if there is an adjective before a noun.
• ​Ex: He is such a kind person.
  

Therefore, the correct answer is option 2).

Additional Information 

• A determiner is a word used before the noun group in a sentence.
• It helps to explain what the noun in the sentence is referring to.
• Ex: Would you like to have this drink?
• Other examples of determiners are- such, this, some, each, etc.